- #1

- 180

- 8

- Thread starter Hertz
- Start date

- #1

- 180

- 8

- #2

mathman

Science Advisor

- 7,877

- 453

http://ptrow.com/articles/Infinite_Series_Sept_07.htm

Above describes the derivation of

$$\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$$

Your equation is readily derived from this. Add all the $$\frac{1}{(2n)^2}$$ terms to your series and then subtract that series as [itex](\sum_{n=1}^{\infty}\frac{1}{n^2})/4[/itex]. You end up with $$\frac{\pi^2}{6}-\frac{1}{4}\frac{\pi^2}{6}=\frac{\pi^2}{8}$$

- #3

- 180

- 8

Thanks!

Last edited:

- #4

WWGD

Science Advisor

Gold Member

2019 Award

- 5,410

- 3,487

I know the proof is written in detail in Dunham's "Journey Through Genius".

- Last Post

- Replies
- 17

- Views
- 3K

- Last Post

- Replies
- 9

- Views
- 3K

- Last Post

- Replies
- 23

- Views
- 1K

- Last Post

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 25

- Views
- 4K

- Last Post

- Replies
- 4

- Views
- 3K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 283

- Last Post

- Replies
- 5

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 708