# Basel problem solution

1. Jun 3, 2010

### hover

http://www.maa.org/news/howeulerdidit.html"
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I found a nice solution to the Basel problem on the internet which I am liking very much. It deals with derivatives and integrals and appears to be a much more solid solution to the Basel problem than Euler's original solution. There is just one thing I am having trouble with to understand the solution. I think it is just me being an idiot but I can't understand the end of the second page,

It sounds like garble and I don't get the logic. Can someone explain to me?

Thanks!!

Last edited by a moderator: May 4, 2017
2. Jun 3, 2010

### LCKurtz

Are you referring to this quote?:

"Any number is the product of an odd number and a power of 2. For odd numbers, the power of 2 is 2^0 . Hence, any square is the product of an odd square and a power of 4. "

All it is saying is that if n is odd, n = 20*n and n2 = 40*n2, which isn't saying much.

If n is even, factor out all factors of 2 so n has the form n = 2pk for some odd integer k. Then n2=22pk2 = 4pk2.

Last edited by a moderator: May 4, 2017
3. Jun 4, 2010

### hover

I'm sorry but I'm still having a hard time understanding. I don't see what the small quote(what I quoted in my first post) is talking about or referring to. The equation above where I quoted says pi^2/8 = ∑ 1/(1+2 k)^2 (n = 0 to infinity). I don't see how euler knows to multiply by 4/3 to get pi^2/6 and solve the Basel problem. :(

4. Sep 28, 2010