#22 Proof Principle of Mathematical induction mathgotserved 1^2+2^2 +3^2++ n^2 nn+12n+1 6

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Prove
1) 1+2+3+...+n=n(n+1)/2 ----------------------------- tinyurl.com/to...
2) 2+2^2+2^3+...+2^n=2(2^n-1) -------------------- tinyurl.com/rm...
3) 1+5+9+...+(4n-3)=n(2n-1)---------------------------tinyurl.com/tp...
4) 1/(1X2)+1/(2X3)+...+1/(n(n+1))=n/(n+1), tinyurl.com/rp...
5) n^3+2n is divisible by 3,----------------------------tinyurl.com/rk...
6) n less 2n----------------------------------------------------tinyurl.com/wp...
7) 1+3+5+7+...+(2n-1)=n^2 for all n in N,-----tinyurl.com/sa...
8) sum Σ k=1 to n k^2= 1/6n(n+1)(2n+1)----tinyurl.com/v3...
9) 9^n-2^n id divisible by 7,----------------------------tinyurl.com/v3...
10) 1+5+9+13+..+(4n-3)=½n(4n-2)----------------tinyurl.com/v3...
11) n Σ k =n(n+1)/2 sum of k n plus one over two---tinyurl.com/wr...
12) 1^3+2^3+3^3+..+n^3= (n(n+1)/2)^2 n^2(n+1)^2/4,-----tinyurl.com/qr...
13) 10^1+10^2+10^3+...+10^n=10/9(10^n-1),----------------tinyurl.com/v9...
14) d/dx (x^-1)=(-1)^nn!/x^(n-1)-----------------------tinyurl.com/sb...
15) 2^n greater or equal 1+n,------------------------ tinyurl.com/tb...
16) 3^n less than (n+1)!,--------------------------------tinyurl.com/tv...
17) 8^n-1 is divisible by 7,-----------------------------tinyurl.com/ud...
18) 10^n-3^n is divisible by 7-------------------------tinyurl.com/wn...
19) 5^n-2^n is divisible by 3--------------------------tinyurl.com/va...
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[@AP-te6mk]

I primarily learn online. I'm sure others including myself have experienced that moment when you hit a snag and it would be great to ask an instructor to clarify the point you're stuck on. You've delivered this lesson in such a way that it minimizes that possibility. This video was clear, concise, and left nothing ambiguous. Thank you so much for taking the time to do this. It was such an amazing help.

[@mathsgotserved]

Thanks!

[@vivekkedar1484]

Fun fact - Everyone one is here cause next day is maths paper 😂😂 I am also here cause tomorrow is my paper in collage 😂😂

[@basetsanakesentseng4526]

Thank you so much, this problem was in my test

[@mathsgotserved]

Glad it helped

[@rohitmallik1416]

Same to you

[@prarthanapramod3861]

THANK YOU SO MUCH. I was struggling with this for hours!!!

[@mathsgotserved]

You're welcome!

[@ajitkumar0872]

I am from India and this is very helpful for me . Well explained sir Thank you so much.

[@mathsgotserved]

Most welcome!

[@kylamoniqueesmeralda2619]

This was the problem that I was assigned! THANK YOU SO MUCHHHH

[@marcjayjaramilloalvarez1470]

Same😊

[@mxh35tcc]

Thank you sooo much sir, this things was not going in my head since 3 months. Thank you!❤

[@mathsgotserved]

Most welcome!

[@AustinAlvaro]

I'll ace MY DMS finals tomorrow

[@Southeducationacademy]

You told that question in very excellent way and every point you explained very well. Thank you so much 🥰

[@mathsgotserved]

My pleasure 😊

[@shadenabdulaziz3388]

Thank you very much! I gotta tell ya, you're incredibly smart.

[@mathsgotserved]

Thank you too!

[@kirthanaramesh9896]

Honestly, this was the best explanation I've heard so far. I like how it is shown step-by-step which is very helpful because some tutors tend to skip some steps assuming we understand the small steps but this is very helpful. Thank you very much! 😀 it is very clear and concise.

[@techg.s.galaris2771]

Hello my friend. Your video is very helpful for my, but i can't find WHY the sum (1^2+2^2+3^2+4^2+ ...... n^2) is equal with [ n (n+1) (2n+1) ] /6

[@leokeatonn]

oh my god thank you this was perfect. The example of what you want the equation to look like in the inductive step before you start writing everything out was perfect, for some reason 99% of vids for this skip that part and it left me so lost.

[@mathsgotserved]

You're very welcome!

[@user-Loubna509]

I am from Morocco Thank you so much ❤❤

[@mathsgotserved]

You are welcome. Morocco is the best 😁👍👍

[@chrisogonas]

Well illustrated! Thanks

[@mathsgotserved]

Glad you liked it!

[@vladyarmolenko-2292]

Thank you so much!

[@mathsgotserved]

You are welcome.

[@princemaphosa4065]

Thank you for a much clearer explanation

[@ravikumar-fw5hg]

Thank you so much it helped me a lot

[@lalitrail]

Nice presentation lucid way to make understand.

[@hilyrics7024]

thank you so much i have been studying this lecture for 4 hours but in vain but his video is like magic I get the lecture now thx sorry for this tras* english

[@srinivasamp8755]

Sir very very thanks for understanding the concepts🙂🙂❤️❤️

[@jameelahahmedlawal4156]

Thank you so much

[@mathsgotserved]

No problem

[@pooja1949]

That was very helpful keep going .

[@mathsgotserved]

Thanks, will do!

[@indhravarma5502]

That was very very helpful, thank you so much 🤗🤓

[@mathsgotserved]

Glad it was helpful!

[@dennislarsen5744]

This was an amazing video. Have a wonderful christmas and keep making videos, you're destined for this!

[@kunalvaishnav9283]

awesome and detailed explanation

[@mathsgotserved]

Glad it helped!

[@divyaprasanababu6273]

How to 7came in that place (k+1) (2k²+7k+6) How can that 7 came in that place

[@nandy8671]

Thank you lot sir I'm most struggled in this problem .....tnq much sir🤝🤝🤝

[@barlonjumburu3597]

Thus wonderful

[@abhinavsuresho5505]

Thankyou a lot sir❤️

[@dineshkumarbhati1406]

Amazing explanation.🙋

[@AMANMUJAWAR-sq6qv]

Thanks 👍🏻 u sir

[@mathsgotserved]

You are very welcome. Take care.😀

[@ammarwrites4933]

Thanks

[@mathsgotserved]

No problem

[@yagn1k]

This video was passed to me 😂 4marks 🇮🇳

[@maazqureshi7441]

Thank you 💝💝😌

[@mathsgotserved]

You are so welcome

[@dabanandamitra5692]

Thank you so much sir 🖤

parabéns

[@GutemaBekele]

where 6 is come

[@angelrojael9592]

Thank you Sir

[@laylabenomar198]

Thank uou🙏🌹

[@mathsgotserved]

You’re welcome 😊

[@luiss428]

im so mad i amde it 2k+1+1 so now its 2k+2 which wasnt correct obvs

[@MuhammadAsghar-vl9fq]

Respected sir , can you please solve the following for me or can anyone help 1^2+2^2+3^2+...+(n-1)^2

[@krishnakumaryadav5563]

Very good video

[@mathsgotserved]

Thanks

[@mohammadbakiir]

Gabisa bahasa engresss;(

[@thabangnkopane4626]

@logician

[@t.b6097]

Anjir nyasat

[@kainaatmakhani6550]

Well illustrated! Thanks

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I'm searching for copper, but i found gold:>>>

[@hanselpeter6009]

Thanks

[@mathsgotserved]

Welcome

[@likongekanyanga7189]

@@mathsgotserved That was awesome

[@likongekanyanga7189]

Thanks 👍 for that good explanation.

[@picklerick1807]

I'm taking Discrete Mathematics at a fucking 4 year university, and this KZbinr is teaching me more than these damn genius professors, office hours, and TAs combined. How sad.

[@zarnihtwe9669]

Thanks. This problem was in my test.🙏

[@mathsgotserved]

Sure

[@CrypStic]

OMG!!! THANK YOU so MUCH! I have my exam tomorrow and this really helping me out. 🥰

[@mathsgotserved]

You are very welcome. Glad we could help.

[@nagpoetries9003]

I m also from india .while my teacher said I can't understand ,but when you say I am understanding .thank you

[@mathsgotserved]

Glad to hear that

[@nagpoetries9003]

Thank you for commenting

[@kpariwuurgilbertb2458]

Great

[@mathsgotserved]

Thanks

[@jackdausan9749]

thanks for this vedio. This concept is awesome 💥

[@mathsgotserved]

You are very welcome.

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Thanks 😇

[@mathsgotserved]

You're welcome!

[@t.b6097]

Nyasar anjir

[@FFI_ZONEGAMER]

Thanku

[@parbatihajong2292]

Thank you 😭 my life saver

[@mathsgotserved]

You are welcome.

[@DarlingHiroXX]

What if we are a given the value of k in question. Where do we insert the value of k then. In your final expression I think

[@techymoh]

I also got some good algebra out of this, besides. thanks.

[@bipinpoudel3863]

Thank you bro😍

[@mathsgotserved]

Welcome 😊

[@nicklouisenacario904]

hoping there was more complex

[@moonshine_edits9204]

Tq.... Sir..... 🔥❤

[@mathsgotserved]

Yw

[@gudurahembra7605]

Thanks u sir 🙏🙏🙏

[@Marianna-ng6he]

Thankyou🙏

[@mathsgotserved]

You’re welcome 😊

[@mdhasibulhossain8040]

Construct proof using mathematical induction of the following: 1 + 2 1 + 2 2 + ⋯ + 2 𝑛 = 2 𝑛+1 − 1

[@ennieguliyev]

Sir, on the left-hand side, it was 1^2+2^2+3^2+......+k^2. And when you explain k+1 part you actually write 1^2+2+3^2+......+k^2+(k+1)^2 instead of just replacing k^2 with (k+1)^2. Why is it? It is easy to understand that you replace k with k+1 on the right-hand side but instead of replacing you have added an extra (k+1)^2 to the left-hand side. For me it is confusing and I do not understand it. Can you explain this if you understood what I meant?