Sum of 1/n^4 (Fourier Series & Parseval's Theorem)

Sum of 1/n^4 by using Fourier Series and Parseval's Theorem,

[roddeguzman]

This is the best gaming channel in youtube hands down.

[sciencifier]

Pikachu I choose


Pikachu 'thunder bolt


'The sum goes from 1 to infinity of 1/n⁴' gets a shock and died


'The sum goes from 1 to infinity of 1/n⁴' is solved

[alexdemoura]

Let me get those people names for a second. To solve a series I need to use:
- series by Fourier: ok, a historical French guy, good one by the way;
- theorem by Parseval: another historical French guy, a bit more obscure, not a knight of Round Table, not Wagner's opera character;
- integration method by Lu Chen the inverse of Chen Lu: both (fictional Chinese???) characters, I didn't find anything relevant on Math in Wikipedia with these names, in order to memorize some Calculus methods;
- praying, may God quotient rule would not show up or probably another (fictional Chinese???) character called Quo Chen Lu should be memorized;
- and now Pikachu, a Japanese manga character...

Too much people for me, almost a Legion to defeat a series.

[rileywells]

I've seen this identity a lot but I've never seen such a nice, elegant proof for it. This video was great, keep it up!

[rajns]

0:09
Pikachu used Stare:
*Its super effective*

[XRyXRy]

yeah, im pikachu:





Pretty
I good
K at
A calculus
C
H
U

[e-money]

The only acceptable way to teach math.

[thomasjefferson]

This was a question on a real analysis exam I had. I really love how this is derived and used. I got that one right. Four years later this has helped me, thank you so much.

[koropol]

you saved me, I needed this proof to write my monography in maths... I'm completely thankful :')

[amritas]

Tears of joy.
I learned Parseval's theorem, Fourier series and odd/even functions -- all from this single video. Thank you for existing, you incredibly adorable Pikachu.

[sensei]

bprp: *wears costume*
audience: *surprised pikachu face*

[Jaojao_puzzlesolver]

0:15 That's the second most lovely Pikachu I've ever seen



The No.1 is of course 0:08

[ajitfhamacademy]

That's very nice . Continue uploading videos like this . It's awesome

[hayzzzeus]

Amazing video! Thanks for helping me prepare for my AP Calculus BC test dad

[ThisIsEduardo]

More videos like this please ! 😂😂😂 I LOVED the costume !!

[AhmedHan]

Is there a general formula for sum of 1/x^n, for all x element of positive integers?

[DjVortex-w]

But I thought Pikachu is a detective, not a maths professor.

[isaacsantos]

Just what I needed to start my morning.

[Supernova]

😂😂😂 the first part. Great video. Saw u first time without spectacles

[benjaminbrady]

I have never seen the fourier series written like that...
Shouldn't it be the sum from t = negative infinity to t = infinity of a_n * e^int
Where the a_n coefficient is 1/2pi integral of f(x) e^-inx dx