What series convergence test do I use?

[@blackpenredpen]

Get the file and the notes first 👉 www.patreon.com/posts/102348401

[@FarukFahmi-h1k]

Sirr does it need for the note you posted a money

[@smokebonde9943]

The video thumbnail reminded me of Organic Chemistry Tutor

[@Archius_09]

at first I taught it was him but then I saw the thumbnail carefully and then channel name

[@mikhaelhalbar417]

OCT is literally god

[@夜神月-l8q]

Broo trueee

[@Andalfulfulde]

​@@Archius_09 that man has no mate😂😂. Five of his kind does not exist on school work. His last video made understood MOMENT OF INNERTIA that I have being struggling with since 2019😂😂😂😂. BlackPenRedpen, You are Legit with Math Also. But that father is un measurable 😢

[@montagecrazy4u]

I got click baited😢

[@blackpenredpen]

Can anyone help me with the timestamps? Thank you.

[@treanungkurmal803]

4:38 Question 1 9:07 Question 2 14:00 Question 3 23:40 Question 4 30:20 Question 5 38:41 Question 6 44:40 Question 7 49:37 Question 8 53:10 Question 9 59:18 Question 10 1:05:25 Question 11 1:10:04 Question 12 1:16:03 Question 13 1:21:03 Question 14 1:28:43 Question 15 1:30:35 Bonus Question Guys the Check pdf in the description for the question. Give a like if you liked the hard work ❤️

[@blackpenredpen]

@@treanungkurmal803 Thank you so much Treanungkur!

[@treanungkurmal803]

@@blackpenredpen Really pleased sir that you replied ❤️

[@jmr0411]

My professor allows us to bring a notecard to the test and I wrote the series convergence tests table you provided on mine. I'm feeling pretty confident, thanks!

[@TheMooseCaboose]

I am going to tear up in happiness as I have never been good with condensing notes to make things less overwhelming. That notes PDF is a game-changer for me. Thank you so much BPRP. I am so happy to have been subscribed to you all these years as you motivated me to become a math tutor. My goal is to make it up to Calc II and this will give me indescribable amount of value!

[@yodelersparadise]

It looks interesting but I can't understand a word you say.

[@ademansor3970]

Can you share it with me please?

[@treanungkurmal803]

Timestamp 4:38 Question 1 9:07 Question 2 14:00 Question 3 23:40 Question 4 30:20 Question 5 38:41 Question 6 44:40 Question 7 49:37 Question 8 53:10 Question 9 59:18 Question 10 1:05:25 Question 11 1:10:04 Question 12 1:16:03 Question 13 1:21:03 Question 14 1:28:43 Question 15 1:30:35 Bonus Question Check the pdf for the questions

[@arpitkeer8114]

Integrate. [Cos^-1x (√1-x^2)]^-1 / Log{1+(sin(2x√1-x^2)/π}

[@thesardaunatv]

If you are interested in mathematics here is my videos on sliderule m.kzbin.info/www/bejne/iJaxd6hqosqChMU

[@aashsyed1277]

almost

[@bubunsaha4120]

Sir from where I can download the pdf of those questions ?

[@ammarkseibi9616]

In question 4, why did you replace sin(2n) by 1? Thank you!

[@AskTig4609]

I enjoy watching your video. It's not just because you are good at explaining things but because we can see it in your face that you really enjoy making this video

[@blackpenredpen]

Thanks!

[@ダーリン-o7t]

omg literally thank you SO much. I know it's been two years since you made this live but it came to my life in the perfect time. You're AMAZING !!!

[@ElReyZero]

BPRP you are a blessing, I have a series test tomorrow and this is helping me a lot to practice!!! Keep up the great content!

[@baseballdude345]

love how enthusiastic this man is about calculus

[@spammusubi1607]

This is EXACTLY what I needed. I’m struggling with this topic at the moment

[@SomethingGamecatAdjacent]

This video was incredible. Used it for my exam last week and it was a CRUCIAL piece of my success

[@mikaelgonzalez2739]

Your good mood is so contagious! Thanks a lot for your clear explanations and giving people like me enjoyment doing this!!

[@robertbrett3350]

Thank you for your kindness by posting many videos for educational purposes. You are good man !

[@delphiaoconnor8544]

watching this in 2023 a day before my calc 2 exam. thank you so much for your videos!! they really help me. btw i'm from nazarbayev university, kazakhstan

[@tomctutor]

Students the _"scary sigma"_ ∑ ☠ takes a lot of practice to master and BPRP has done a marvelous job here putting this material together covering all the various tests you need to know. ✔ *BonusQ:* LCT: [sin(1/2n)]^2 ,which is monotonic↘, with lim n→∞ of p-conv (1/(2n)^2), let ⌀=1/(2n) so lim ⌀→0 [sin(⌀)/⌀]^2=1.

[@glen8826]

Super proud of myself of going through this start to finish

[@mr.explisovesnowman8836]

thank you balckpenredpen............. for posting this days after my exam.... but seriously good video

[@roberthaas3376]

Hey! I just wanted to say thank you so much for this stream, my exam is in about 3 hours and I found this gem last night and binged through it. I feel so much more confident now!

[@ioannischrysostomou7012]

How did you do

[@roberthaas3376]

@@ioannischrysostomou7012 Yeah.... I failed

[@patrickhaynes2394]

Someone who truly loves math, I found my polar opposite.

[@guilhermevolpini6136]

Saved my calc 3 test ❤

[@skwbusaidi]

Number 14 Can also be expressed as sum from 2 to inf of 1/(n^2-1)

[@spb1179]

Thanks for this, test over it tomorrow!

[@anstjd_ys]

You are the legend, always the best explanation

[@opufy]

THANK YOU! for that gift note!

[@amandastandow8912]

BLESS! These notes are going to make my homework downright bearable!

[@kingarth0r]

44:22 thanks for the shout out my guy

[@theclown6217]

Ey thas my friend

[@adrianoseresi3525]

A truly fine beard my good sir!

[@OgundipeSamuel-cp6xt]

You really motivate me and I wish to meet you in person someday 😊

[@AngelCampa-im4to]

your amazing!!! you make this really easy to understand and follow along !!

[@dasav6724]

Yo blackpenredpen! For your next 100 problem challenge, could you tackle trigonometric equations and identities and stuff? Basically, formulas like sinC + sinD, the half angle formulas, and all that good stuff used in simplifying and solving problems. Thank you for everything.

[@blackpenredpen]

That's on my list! : )

[@carolynncalin1199]

YOU ARE AMAZING!! You are saving my calc II grade in university.

[@rantongl2238]

Bro if I pass my first analysis test in uni it's all because of you. Thank you so much for the content!

[@krrishmaheshwari4860]

13 Question , i think it is conditionally Convergent as |Un|=1/n(3+1/n) where by p series p=1

[@violintegral]

I have a test on Sequences on Series due today (I'm taking Calc 2 online through my local community college since I'm still in high school) so I'm using this video as a final review. I already watched it through once a few months ago when I was teaching myself, but I'm back again!

[@sabrinaf4436]

Thank you from Italy!

[@djomoangeingrid6923]

I'm currently doing real analysis and this video was soo helpfull thanks so much

[@nicholaschow6389]

i have my calc 2 final exam in 4 days bro actually saved me

[@The1RandomFool]

On the bonus question at the end, a bit of analysis can also be used. You can use the comparison test with the sum of 1/(2*n^2), which means the series converges to a value less than or equal to pi^2/12. The reason for this is because you can use the series expansion of 1 - cos(1/n) to get the sum of 1 - (1 - 1/(2*n^2) + O(1/n^4)), which simplifies to the sum of 1/(2*n^2) - O(1/n^4). It's less than or equal to the sum of 1/(2*n^2).

[@violintegral]

Even easier: notice that 1-cos(1/n)=2sin²(1/(2n)). This converges by #9 on this video, which showed that sin²(1/n) converges by the limit comparison test with 1/n². Since sin²(1/n) is always positive and it converges, then it does so absolutely. Since it converges absolutely, then any rearrangement of its terms also converges absolutely, and to the same value. Therefore, the sequence of even terms of sin²(1/n), sin²(1/(2n)), must also converge. Or you could just do limit comparison with 1/n² again lol. You basically did the same thing anyway, but it's even easier if you just use the trig identity so you don't have to worry about the Taylor Polynomial approximations and such.

[@girijasankarmandal1138]

Your pdf is very very helpful to me sir thank you for your effort for us.

[@JamesSmith-fl6pd]

Thank you so much you saved my life!

[@blackpenredpen]

Happy to help!

[@arpitkeer8114]

Integrate. [Cos^-1x (√1-x^2)]^-1 / Log{1+(sin(2x√1-x^2)/π}

[@The1RandomFool]

For number 3, the root test would work as well, and includes a famous limit (n!)^(1/n) / n as n approaches infinity.

[@andrekpl7668]

Great job man

[@nvapisces7011]

For bonus question, can use the double angle formula to change it to 2sin²(1/2n). Last we recall, there is a similar question earlier where we use limit comparison test for 1/(4n²)

[@andreasavraam6898]

If the ratio test is inconclusive, you might be able to use Raabe's test (of course it's not certain that it'll be conclusive either). You could add it in the notes after the ratio test.

[@andreasavraam6898]

It basically says that if the ratio limit is equal to 1, calculate the lim of n(1-an+1/an),let's say that this limit is equal to L, then if L>1 then the original series converges,if L

[@ashleychandler3642]

Life saver! Thank you so much.

[@mirayayna1295]

From Lebanon 🇱🇧 Thank you very much❤️

[@elie.makdissi]

Heyy there i'm too from Lebanon! Are you in uni?

[@mirayayna1295]

@@elie.makdissi yes

[@mirayayna1295]

@@elie.makdissi first year Engineering At USEK

[@elie.makdissi]

@@mirayayna1295 Ah cool gd luck!

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Hi me to arabic but I'm from morocoo

[@pizzy1992]

This was just wonderful :D thanks a lot

[@pierrevieu9997]

Ratio test is called d’alembert rule in 🇫🇷

[@mohsinqureshi6526]

So nice teaching bro .. thank you so much .... 👍🏼

[@spacee3249]

Abbreviation may change between teachers for the final test explanation (problem 4), but this is very helpful! Thank you bprp

[@nicogehren6566]

very helpfull video thanks Mr. bprp

[@Bravo_L]

This is awesome thanks professor!!!!!!!

[@davida99]

This is good practice for my final!

[@PhysicsofAcala]

your videos are amazing. Thank you.

[@yzotape529]

WHY WAS THIS NOT RELEASED 4 DAYS AGO WHEN I DIDNT HAVE MY CALC 2 EXAM ON FRIDAY -purdue engineering student

[@dylant830]

Haha I really could have used this practice before I failed my calc final yesterday :)

[@jmr0411]

I have mine today luckily

[@darcash1738]

5 can also be done by integral test

[@nigelsheldon5753]

Thank you! You're the best!

[@krrishmaheshwari4860]

Bonus Question: 1-cos(1/n)=2sin^2(1/2n) multiply divide by 4n^2 take limit sinx/x=0 as x-->0 we will be left with 1/n^2 variable term which we can take as vn now un/vn=1/2 hence by P series Vn is convergent and so is Un! :)

[@prudvigorantla930]

How to limit X tends to zero sin(X) also tends to zero. In problem no 9

[@alainrogez8485]

For the bonus, I used Taylor series. Cos u = 1-u^2/2. So 1-cos(1/n) goes to 1/2n^2. Thanks to the p-series, because p is equal to 2 in this one, the bonus serie converges.

[@tusharkhatri5795]

Cos(1/n) at n tends to inf =1 hence divergent

[@cina0rh]

This is amazing thank you

[@wjrasmussen666]

Another great video!!

[@ahmedismailfahmy4365]

bonus >> LCT with 1/n^2 , it will converge

[@riazuddinsheikh3198]

No. It will diverge by LCT taking 1/2n

[@juice_verse]

@@riazuddinsheikh3198 You mean diverge by using LCT, and comparing by 1/2n

[@jameskennedy674]

This guys dope. I like him!

[@anjanamarasinghe6623]

Thank you very much.clear and sweet.

[@87AndreasW]

Are you able to give some information about dynamic systems? matrices etc. I have this question but unsure what to put as X1, Y1 and X2,Y2 "David jogs either in the woods or on asphalt. If he jogs in the woods, the probability is 30% that the next jogging trip is also in the forest, while the probability is 70% for the next jogging trip on asphalt.If he jogged on asphalt, the probability is 50% that the next trip is in the woods, and 50% the first trip on asphalt. David jogs his first trip in the woods. Find a formula for probability vector k, which describes the probabilities of forest or asphalt on trip k."

[@BrawlN64]

Float vs Natural Number vs Integer Range divided or not by consant vs fractional sets vs OE set vs Complex numbers vs Phasors how fast/ops for convergence vs error cases 1/INF=Infintesimal 10bit 1/INF=0 32bit

[@jojodalmangadijojo]

Preparing for analysis 1 exam in IT For the number 12 I did a Limit comparison test with 1/n²+1, which converges because it's less than 1/n² which, again, converges because it's a p series where p>1. So from the LCT I got π/2>0, so the 12 converges too. The solving should be correct, so yay I found another way which, to be honest, seems way easier than getting the graph, taking the integral et cetera.

[@negar1370]

Thank you so much!

[@ffc1a28c7]

For 12, you can just do direct comparison test with pi/(2x^2) which converges as arctanx is bound by pi/2.

[@kateryna1611]

Thank you so much!!!

[@btsfan69420]

I have my final exam tomorrow. I’m channeling my bprp knowledge before bed with this video

[@denisedesireeannaneumann9804]

Thank you 🌈👌

[@xgs660]

Wow I have an exam of series tomorrow thanks😂😂😂❤

[@NoName-eh8fz]

I have 2 questions. Im not studying maths yet (Im still in school) so I dont know if my ways of solving are correct. Would be really cool if somebody could verify or show the mistakes. Question 12 arctan(n)

[@violintegral]

Your method for #12 is close but not correct. Notice that arctan(1)=π/4 and arctanx approaches π/2 as x→∞, so arctan(n)

[@subhajit201]

Only if I had u as my maths teacher during my grad.

[@kiranbarnwal8503]

In question no 3 14:00 -2/e is correct as minus sign will remain with 2

[@myraniang3649]

no, because of the abs value

[@PimpMatt0]

I had to learn this in a week over summer 😩 damn now I forgot it all

[@girijasankarmandal1138]

n4+3n/4n3-2n+1 divergence or convergence

[@brucefrizzell4221]

What could make BPRP better ? Subtitles for SIX languages . Math Fhein a Thidseir . Well done Teacher .

[@luciennyuba4980]

Thank you professor, keep up the good work

[@academicmood]

Damn you make me miss math

[@ahmedoran8886]

Loov maht

[@wuznab5109]

I must be extremely dumb, but I still don't understand when and what types of series to apply to problems. As far as i can tell there is no general rule in knowing which one to use. It all has to be memorized??? Can someone please help me out, there has to be some pattern here i'm missing?

[@phazonicridley3858]

Bonus question answer. Converges by DCT compare it to 1/(n^2) (a convergent series) which is bigger than 1 - cos(1/n).

[@phazonicridley3858]

Ps: thank you so much for this video!

[@alainrogez8485]

Q bonus : use Taylor series. 1 - cos (1/n) = 1 - 1 + 1/n^2 + o(1/n^4) Equivalent to 1/n^2 serie which converges.

[@amjc6271]

wow!, I appreciate you

[@nvapisces7011]

Now that I've learnt calculus 2, I can do these questions. Question 12 looks challenging looking at the live chat just guessing and using integral test. I would say use direct comparison test. The series is obviously less than or equal to the series (pi/2)/(n²+1), which is less than or equal to the series (pi/2)/n², which converges by the p series test. By direct comparison test, original series is smaller so it converges as well Ok nvm integral test can be used but in my exam i have to show that it is positive, continuous and decreasing to use it. Don't really need to show it is positive side it is obvious but we have to show that the limit as x goes to a is f(a) to show it is continuous. Then to show it is decreasing we either use a_n

[@lichen420]

I thought that if cos(0) is 1 and cos(1) is about 1/2 you would be adding closer and closer to one and the sum would be divergent.

[@charlesdesouza9313]

what is this useful for? i mean, applications instead of memorizing?

[@hectortroncoso322]

Im Hector Troncoso;65 years old;this tutorial makes me remember thats very happy days when professors gave me all this knowledge,and i find here the difficulties of my poor english;so ,please ,could you speak a little more slow and clear,if it dont disturbs you? Here in Argentina,we speaks spanish idiom. Thanks you for share your knowledge,i think that nature gave you this kind of mind that permits you to see with brain.Go ahead!

[@juice_verse]

The last one Converges by the limit comparison test, where we compare it to 1/2n(theta), and the cos(2theta), we end up having 2Sin(1/2n)*Sin(1/2n)/1/4n^2 as n-> infinity, which converges to 2. Am I right?

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I love this video

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I do not understand the holdning of the ball. What is it? A speaker?

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Hey, thank you for your videos, just the link of the file says it got blocked by bitly, do you have another one?

[@AMIT_OP]

Nice beared sir

[@girijasankarmandal1138]

Can you please make some vedio on 3-d geometry

[@muroderepolho69]

Thank you :D

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loving the beard!