#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!

[@dennislarsen5744]

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

[@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😊

[@vladyarmolenko-2292]

Thank you so much!

[@mathsgotserved]

You are 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!

[@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

[@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.

[@Southeducationacademy]

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

[@mathsgotserved]

My pleasure 😊

[@princemaphosa4065]

Thank you for a much clearer explanation

[@shadenabdulaziz3388]

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

[@mathsgotserved]

Thank you too!

[@hudaesports]

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

[@lalitrail]

Nice presentation lucid way to make understand.

[@zarnihtwe9669]

Thanks. This problem was in my test.🙏

[@mathsgotserved]

Sure

[@ravikumar-fw5hg]

Thank you so much it helped me a lot

[@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!

[@jackdausan9749]

thanks for this vedio. This concept is awesome 💥

[@mathsgotserved]

You are very welcome.

[@pooja1949]

That was very helpful keep going
.

[@mathsgotserved]

Thanks, will do!

[@kunalvaishnav9283]

awesome and detailed explanation

[@mathsgotserved]

Glad it helped!

[@srinivasamp8755]

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

[@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

[@markjamescruz8957]

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

[@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.

[@parbatihajong2292]

Thank you 😭 my life saver

[@mathsgotserved]

You are welcome.

[@nandy8671]

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

[@jameelahahmedlawal4156]

Thank you so much

[@mathsgotserved]

No problem

[@dineshkumarbhati1406]

Amazing explanation.🙋

[@picklerick1807]

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

[@maazqureshi7441]

Thank you 💝💝😌

[@mathsgotserved]

You are so welcome

[@indhravarma5502]

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

[@mathsgotserved]

Glad it was helpful!

[@krisensiyasitohang544]

Thanks 😇

[@mathsgotserved]

You're welcome!

[@dabanandamitra5692]

Thank you so much sir 🖤

[@abhinavsuresho5505]

Thankyou a lot sir❤️

[@bipinpoudel3863]

Thank you bro😍

[@mathsgotserved]

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

[@moonshine_edits9204]

Tq.... Sir..... 🔥❤

[@mathsgotserved]

Yw

[@divyaprasanababu6273]

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

[@LensonZachariah]

Impressive 🥰🥰🥰

[@barlonjumburu3597]

Thus wonderful

[@yagn1k]

This video was passed to me 😂 4marks 🇮🇳

parabéns

[@techymoh]

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

[@FFI_ZONEGAMER]

Thanku

[@gudurahembra7605]

Thanks u sir 🙏🙏🙏

[@Marianna-ng6he]

Thankyou🙏

[@mathsgotserved]

You’re welcome 😊

[@laylabenomar198]

Thank uou🙏🌹

[@mathsgotserved]

You’re welcome 😊

[@hanselpeter6009]

Thanks

[@mathsgotserved]

Welcome

[@likongekanyanga7189]

@@mathsgotserved That was awesome

[@likongekanyanga7189]

Thanks 👍 for that good explanation.

[@nicklouisenacario904]

hoping there was more complex

[@krishnakumaryadav5563]

Very good video

[@mathsgotserved]

Thanks

[@kpariwuurgilbertb2458]

Great

[@mathsgotserved]

Thanks

[@angelrojael9592]

Thank you Sir

[@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

[@GutemaBekele]

where 6 is come

[@luiss428]

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

[@mdhasibulhossain8040]

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

[@mohammadbakiir]

Gabisa bahasa engresss;(

[@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?

[@thabangnkopane4626]

@logician

[@johnchacko96]

❤

[@t.b6097]

Nyasar anjir

[@t.b6097]

Anjir nyasat

[@kainaatmakhani6550]

Well illustrated! Thanks

[@AMANMUJAWAR-sq6qv]

Thanks 👍🏻 u sir

[@mathsgotserved]

You are very welcome. Take care.😀

[@ammarwrites4933]

Thanks

[@mathsgotserved]

No problem