You Should Learn This Trick!

[@brain_station_videos]

You can support our work at www.patreon.com/BrainStation

[@whom_you_never_look_for]

Simple , skip this 1 mark question

[@Mystery-qp5kn]

Looser mentality It's my mentality

[@linconplayz9643]

bro cured my brainrot and left me thinking

[@GamerIntrix]

With binomial theorem of non natural index. This can also be solved (50/49)⁵⁰ ×1/49 = (1/49 +1)⁵⁰×1/49.. (1+x)^n = 1+nx + n(n-1)/2 +......

[@AVR0709]

They are natural indices though. You can directly use the binomial theorem for natural indices.

[@SelflessCaptain45]

I don't know to solve this with binomial lol😂

[@colitipal]

As n approaches infinity: (n-1)^(n+1) > n^n

[@thecarman3693]

Actually it becomes true once n > 4 with 'n' being an integer. From just 5 onwards it's true, no need for such large values. And for n = 4 or less (4, 3, 2, 1) you need to reverse the greater-than symbol to less-than.

[@WinspaceWS]

​@@thecarman3693this is why he said as n → ∞, (n-1)^(n+1) simply grows faster than n^n

[@thecarman3693]

Interesting ... because 1^1 > 0^2 and 2^2 > 1^3 and 3^3 > 2^4, and 4^4 > 3^5. But with 5 we get 5^5 < 4^6. So there is a value for 'a' that works for a^a = (a - 1)^(a +1) where 4 < a < 5. Any takers? As for the given problem, 49^51 is over 17.8 times greater than 50^50.

[@nothing0x4D2]

Just a different way to compare these values, Given 49^51 and 50^50 Taking the natural log of both: 51ln(49), 50ln(50) Which can be written as: (50+1) * ln(50-1) Lets assume both of these are functions as both values change. x * ln(y) Now, d(xlny) = lny dx + x/y dy, in this case x = 50, y = 50 and delta x = 1, delta y = -1 putting in all the values: delta = ln50 - 50/50 = ln(50)-1 > 0 (the actual delta would be bit diffrent and this is just an approximation and we only care if the net delta is positive or negetive) So since the delta is positive, 51ln(49) is bigger. This can be generalised for case where x=y: delta = lnx - 1 so delta is positive as long as x>e. And this can be used as a general result. Similar conclusion can be achieved by taking log of the initial inequality , and comparing rate of change of logarithmic and linear graphs.

[@bineshsukumaran1994]

This is the first thought that came into my mind. Why not use log.

[@Redstoner34526]

Very good solution of what initially looks like a tricky problem!

[@GOJO_SATO]

Thats what i did to solve this I set the 50^50 into (49+1)^50 And now i used binomial theorem to find out (a+b)^x Same with 49^51 So this is probably gonna get buried but let me say How i solved this I converted into (50-1)^49 And then used the binomial theorem again ... To find (a-b)^49 Then i compared both of them and got my answer I know this is very long and complicated process ... But this was only way i knew

[@ranveerdrablani5656]

Oh nice

[@GOJO_SATO]

@ranveerdrablani5656 hmm Reading the comments bro I feel like binomial theorem was the best way to find this What do you say ?

[@ranveerdrablani5656]

@@GOJO_SATO same there has to be a more effective way tho but its going to take some finding

[@GOJO_SATO]

@@ranveerdrablani5656 hmm let me do some research about this I'll contact you after a few hours Do you use insta or something social media so ?

[@MicahFranco]

@GOJO_SATOi just did it in my head. And i used a smaller number, like 10^2 < 9^3

[@aniketb2010]

Feels like revisiting school days. :)

[@fuzrohdah]

49^51 is simply 49 × 49^50. It's easy to think that 49^50 and 50^50 aren't very far away. However, the former is 49 times more and thus will be a much bigger number than the latter.

[@ctcboater]

This guy can't speak math. Is it a robot?

[@CruisygamingwithMokshaSaini]

AI

[@SiLentEditz005]

We could have used logarithmic calculation

[@kinulidd0598]

no calculator allowed

[@markrobinson9956]

You can calculate logarithms easily on a slide rule.

[@Federer.]

no calculator needed It’s just simple multiplication 0.8451*2*51>50(0.699+1)

[@sleepdepriveduser]

​@@Federer.explain please...

[@totiodfanzsai6079]

Ofc, a difference in power is a literal multiplier and same difference in base is almost nothing in comparison so it's pretty obvious for large no.s

[@kaamiKunn]

This is the logic is used too hahaha

[@david_flak3036]

Hm, i went in a really simple way, but also reached the correct answer. 49*51 is 7*2 squared again to 51, multiply the exponential and it's 7*102 Using a tricky to find the square root of 50: 50+49/2×7 equals to 7,07 Then, 7,07*100 is smaller than 7*102.

[@saucepano6155]

you did nothing, how do you know its smaller

[@david_flak3036]

@@saucepano6155 by taking the root of both and multiplying the exponential by two and reducing by 100, 7,07^0 is smaller than 7^2

[@david_flak3036]

By going to the calculator it is smaller anyway

[@saucepano6155]

@@david_flak3036 are you dumb

[@geralynpinto5971]

Thanks so much. Yes, indeed, it is so good!😊

[@pion137]

AI content. The function f(n) = n^n - (n-1)^(n+1) is only positive and increasing for the first few terms and then plummets. Meaning the right most term will always be larger.

[@RobinLindhNilsson]

Wow! Thanks for this really amazing trick, I am sure I will remember this fast easy way and that it will come in handy some day ❤😂

[@dkrishna2868]

Write 49 as 50-1 then binomial expansion

[@SelflessCaptain45]

I just did 5x5, 49x5 logic. 49^51 is greater.

[@RyanLewis-Johnson-wq6xs]

(1+1/3)^3=64/27=2.370 recurring

[@АлександерСемёнов-ц2н]

2¹⁰/²⁷*

[@leif1075]

What does that jave tomd0nwothbtbis problem?

[@infrences]

@@leif1075Further explanation of how (n+1/n)^n increases to euler’s constant

[@nukefiter9996]

Love these ids :) I tricked the whole class into thinking that I was a human calculator with these videos.

[@Edgar-e4u]

God work pal.

[@Speggtacular_egg]

I solved it like this: The ratio between 50 and 49 is very small, so having one more power would mean that one number is significantly bigger than the other, thus making a big difference, which leads me to conclude that 49⁵¹ is greater than 50⁵⁰

[@dumeu5731]

And where proofs or any mathematics conclusions? You are using intuition and your life experience, not really doing math

[@markrobinson9956]

I feel like logarithms could be useful here.

[@King58468]

Awesome solution

[@jutubesku5584]

I took a screenshot from the clip, pasted it to Photoshop and compared sizes of theese numbers. The answear is: 49^51 is bigger!

[@brain_station_videos]

😆

[@UmairAhmed107-rt9ub]

Great sir , please bring more videos like this❤❤❤

[@cynx1321]

50+50=49+51 50×50>49×51 (2500>2499) 50^50

[@blitzy_girl]

gd player cynx

[@cynx1321]

@meowBlitz how da f

[@Usernamein2]

I just realized that x² is equal to (x-1)*(x+1)+1

[@kebapgaming]

@@Usernamein2true

[@AncientPros]

Bro this logic doesn't make any sense

[@RyanLewis-Johnson-wq6xs]

Limit[(1+1/n)^n,n->∞]=e Input lim_(n->∞) (1 + 1/n)^n = e Result True

[@looksmaxxingmastersigma]

bot

[@RoyalRed-mh6bz]

We know that 50^50 > 49^50 Wich means 50^50 < 49^50 × 49 Because 49×49 is bigger then 50 And 49^50 × 49 = 49^51 Wich means 50^50 < 49^51

[@shivangssinha1915]

Nice trick💯👍.

[@sibinipriyadarshini7224]

Use logarithm of both sides and compare

[@kasusista3317]

Why not take a log of the two? 50 log50 vs 51 log 49?

[@Swaritz13]

how would u solve further?

[@tugradd8961]

@@Swaritz13with the knowledge of logarithms, 102 times log7, 7 is lower than 10 so this is smaller than 102. Log50 is log5 + 1 so 50 times log 50 is larger than 50. There is a chance that you predict it wrong but with numbers like these, your prediction will most likely be true

[@SimpCe]

Just read the replies buddy.

[@ZenithBreeze]

Doesn't necessarily work. 4⁴ shouldn't be greater than 3⁵ if this was true, but unfortunately 4⁴ = 256 and 3⁵ = 243. Even though 3⁵ has one more power, it is not greater than 4⁴. Although if you do this with any number larger than 4, you are indeed correct.

[@faheem-p7q]

So does that mean 2^3 is bigger than 3^2?no,its not that straight forward for some people and its kinda useful that he is going over this for people who are trying to learn and understand the many topics/concepts maths has and videos like these help to build that understanding.

[@SimpCe]

Well in most cases like this it works

[@jaikadam6683]

My friend its not about getting the answer its about how you do it

[@Fadexpl]

​@@SimpCe ah yes, my favorite type of proof. Guessing. You're not doing math, you're guessing.

[@Sakuya_Izayoi99]

Log50=Log10+Log5=1+.689=1.689 Log49=2log7=2*.845=1.69 Therefore,51*1.69 and 50*1.689, which one is larger?

[@Axomight-01]

How to calculate values of log Like u did Log10 = 1 and Log5=0.689 Did u use log table?

[@Sakuya_Izayoi99]

@ Well, I just remember some values of log, e.g., log2, log3, log5, log7, log10. In Taiwan, they always put these on high school math exam papers, because they ask us to solve the log problem by hand, not calculator. So actually, I saw them several times, and I still remember them, even though I haven’t touched high school math in almost 13 years. (I’m a account manager, in my job, only can touch the basic level math XD)

[@ayberkm]

This video cured my insomnia

[@ayushrajroy3_123]

Log50^50 =1 Log49^51=log49^(49+2)=log49^49+log49^2 Now log49^49=1 log49^2 be some integer greater than 0 So it will 1 + something Now, 150^50😅 simple for iitain

[@tejas_2822]

Log (50^50)=1?? It would be 50 log (50) Similarly it would be 49log49

[@ayushrajroy3_123]

@tejas_2822 not log 50 to power 50 log 50 with base 50

[@davidc1179]

x^y = x ln y so... 50 ln 50 ? 51 ln 49 ln y grows more slowly than y = x when y is larger than 1. So, is average number times average number smaller or larger than very big number times slightly less than average number ?

[@Quakeboy02]

The easy answer is to understand that 1 raised to infinity is still 1.

[@damianwrobel5715]

1^99999999999 = 1 but 1^infinity = indetermined symbol (We don't know exactly how much is it. We should take the limit and do the calculations to know if this particular expression if the form "1^infinity" tends to infinity or if IT tends to a number).

[@Quakeboy02]

@@damianwrobel5715 You don't really have a good understanding of raising 1 to any power, do you? OK, here's a test: What is 0^999999999999999 ? Do you think that is zero, or does it tend to some other number?

[@lordturkey8324]

or you can use common sense and realise the second number has a greater exponent, while the other has a greater base. 9 times out of 10 the greater exponent will be bigger

[@RyanLewis-Johnson-wq6xs]

(1+1/1)^1=2

[@khalief_.]

oh well atleast i learned new things

[@RyanLewis-Johnson-wq6xs]

(1+1/2)^2=2.25

[@MutalibGozalov]

50^50 / 49^50 = 2.746 => means 50^50 is *2.746 times 49^50* . 49^51 / 49^50 = 49 => means 49^51 is *49 times 49^50* . 50^50 / 49^51 = 2.746 / 49

[@Dongadonga-y4d]

How to work with mixed fractions

[@arnavray4551]

@everyone double tap this comment and see the magic.🤣🤣 I like your videos 😎 . Nice trick.👍🏻

[@Hellothere5-dr4uj]

I also like his videos 👍

[@Am-jx9qk]

hmm.....

[@vaibhavchoudhary9942]

Na using binomial theorem will take only about 10-15 secs to solve this ques

[@GOJO_SATO]

Same thing i did

[@sonu-he3hn]

Can't we use binomial theorem😅

[@Aditya-Roy]

Use log

[@alien3200]

How do you even know, you have to begin like this

[@brain_station_videos]

Practice

[@leif1075]

​​@@brain_station_videosI don't think it's practice though truly. Don't you agree this is too.co trived and no one will.think of.tbis even if they have seen logs before? Why would they? I don't think there's a valid reason to. Taking logs of.both sides maybe but not this? What do you say? Thanks for sharing.

[@jeffw1267]

I would stipulate that logarithms can't be used to find the solution, because it greatly simplifies the problem if you can use logarithms.

[@raptorthegamer5524]

thats the point

[@antoniopedrofalcaolopesmor6095]

But if you use logs you will then need a calculator to compare the numbers, right?

[@leif1075]

​@@antoniopedrofalcaolopesmor6095not necessarily you can do with pen and paper then it's not cheating

[@spg9461]

Just use logarithm (preferably base e or 10)

[@xgamerxplays9205]

Why spend all that time when it’s only 50/50?

[@n.p.9997]

Euler ❌ Oiler ✅

[@m.qy_ht]

the greater number is the one with the greater exponent logical thinking. :/

[@brain_station_videos]

Ok so 2^3 (8) is greater than 3^2 (9)? Nice 👍

[@Chloethecoolestytr]

All i did was 50x2 = 49x3 100 = 147 Not really that great but I’m lazy lol

[@bowxfire5275]

I did 3^3 compared with 4^2 and decided 3^3 is larger lol. Fluke but a w is a w 😂

[@syed3344]

I use derivatives

[@hvnterblack]

too chaotic

[@semka6378]

решил за 0.01 секунду по правилу "степень пизже основания"

[@Farmhr]

take log both side

[@𠅇]

that ai profile picture 💀💀💀💀

[@vivekmohan3981]

Or do what I do - if it seems like the unlikely answer, it IS the answer :-/

[@KavinduPrabhashwara-bk3rp]

Dude do you really need that much steps to get the answer? Can’t you see it when you look at it in first glance 49*49=2401*49=117649 and 50*50=2500 then I can say 50**(n-1)

[@Fred-rg5vw]

Why not just use a calculator when much faster ? Cool maths tricks are cool when they save time..this clearly doesnt so kinda pointless imo.

[@brain_station_videos]

Ya I got the point and I respect your opinion! But then why learn math at all ... like why should we learn to solve equations etc when we have online equation solvers to do the same 😗 We do this to train our brains, improve problem-solving skills, and develop logical thinking that goes beyond just getting the answer. 😊

[@Fred-rg5vw]

@brain_station_videos OK that's fair enough too. I guess I just personally prefer the kind of mental math tricks/ shortcut things. That lead to answers / good approximations. That's prob cause that's what I'm good at and that it's enough in vast majority of situations in everyday life..if you're not an engineer or physicist for eg. I defn could do with some practise in other areas tho so will check out more of your vids. Cheers

[@amirkhursheeddar]

Just use log

[@拗拗拗拗]

To be honest I would just use log

[@LuffyTaro486]

Or, 50^50 o (49^50)*49 =50^50 o 2401^50 Since 50, 2401 > 0 Therefore 50^x < 2401^x if x is positive, and 50 is positive So, 50^50< 2401< 50 Or, 50^50

[@brain_station_videos]

Nope... (49^50) * 49 = 49^(50 + 1) = 49^51 2401^50 = (49^2)^50 = 49^(2 * 50) = 49^100 so, (49^50) * 49 ≠ 2401^50

[@LuffyTaro486]

@@brain_station_videos oh ok

[@RyanLewis-Johnson-wq6xs]

50^50

[@Vibelofi-j3r]

Big Bro your channel is monitize or not

[@Korsa_sfm]

ello brain station! i love ur vids

[@fatyotherabbit4139]

Crazy

[@VickyKumar-ys6bg]

Right now the views are 77777 😱😱

[@kingdemogame2604]

есть такая теорема - степень пизже основания

[@idmarkvlasov]

Только трушные ребята знают, что степень пизже основания

[@RadheKumar-c4q]

its ea_y 50

[@the_Dark_Knight_12]

Brilliant

[@steveparsons6719]

Computer generated narration simply does not work for maths videos. At least not this one. Please narrate yourself or - if you must - find an AI that’s up to the task.

[@antoniopedrofalcaolopesmor6095]

What's wrong with the narration? It's crystal clear, a lot better than having to listen to some weird pronounciation, right?

[@antoniopedrofalcaolopesmor6095]

The narration is crystal clear, I could not ask any better

[@steveparsons6719]

​@@antoniopedrofalcaolopesmor6095 Since you asked, I steeled my ears and listened to this several times to make a list for you. You will see that there are around 31 mistakes, instances of contrived wording, and poor edits, in a video containing less than 4 minutes of content. It's very distracting to the brain to have to listen to one of these every 8 seconds or so, and diverts the attention from the interesting mathematical principals it is trying to convey. DETAILS The use of "50 to the 50" (rather than "50 to the 50th", or "50 to the 50th power") and similar, throughout, is annoying to my ears, but I guess may be standard elsewhere. Similarly "50 raised to 50" etc, such as at 0:04, 0:08, 0:30, and in my final comment. (I have not counted these among the 31). 0:44 - missing THE in "now we will only work on ___ left-hand side". 0:50, 1:12 - missing THE in "using ___ power rule". 0:54 - superfluous "th" after "times 49". 1:03 - missing pauses: "raised to 50 times one upon 49" sounds like the whole thing is the exponent; there should be pauses before and after "times". 1:16 - same mistake as 1:03. 1:24, 1:42, 3:05, 3:13, 3:15, 3:26 - "49 square" should be "49 squared": the AI is presumably thinking of "miles square" or another unit, rather than figures. 1:38 - "whole raised to 49" is contrived; "all raised to the power of 49" would be the natural way to say this. 1:51, 2:06 - "whole raised to n" - same contrived wording as 1:38 etc. 1:57 -

[@mkadx2136]

50^50=(49+1)^50=49^50+1+98 =49^50(1+99/49^50) and it is so clean to know who greater , 49^51 =49^50 • 49

[@navinkumar4339]

(a+b)² formula didn't apply here bro It's (49+1)⁵⁰ not (49+1)² both here you have taken 49⁵⁰ +1 correctly but 49×2 is wrong here

[@suhnih4076]

Wow

[@99Unknown]

Can you solve IIT physics questions ☠️☠️

[@BeastStudio7]

In my first seen I say They both are equal

[@OnDaTrainToMath]

HI

[@BiRyunyeon]

But the answer is wrong tho?

[@wirmaple7336]

how come?

[@BiRyunyeon]

@@wirmaple7336 I checked it on Gemini since i taught it doesn't make much sense

[@BiRyunyeon]

@@wirmaple7336 i googled

[@Mx_Refire]

wow

[@btsarmyboy450]

First 😊

[@TheNumberblock3.275]

50^50=8.882×10⁸⁴ 49^51=1.585×10⁸⁶ 50^50 < 49^51

[@JarppaGuru]

one that have more on exp bcoz values are close 49^50 3,2344765096247579913446477691002e+84 50^50 8,8817841970012523233890533447266e+84 49^51 158,48934897161314157588774068591e+84