Hello, soyeahiknow!
It is a major theorem that:
. .
Use this to calculate: .
We have: .
. . . . . . . .
. . . . . . . .
. . . . . . . .
Are the denominators primes? .
or a Fibonacci-type sequence? .
Prime Zeta Function -- from Wolfram MathWorld
id:A085548 - OEIS Search Results
EDIT: I should have added some comment to be clear; it's likely that tonio is right that the problem is misstated; nevertheless, if it is correctly stated then the above links are relevant.
In post #2, Soroban factored out (1/2)^2 because it evenly divides each term, and because doing so allows us to express the sum as a product of already known quantities.
For this problem, think about what happens when you add this series to the series that Soroban solved.
if I add this series to the one Soroban solves, it would just be back to the original series right?
OOOOO so all I have to do is ( original series - series with all the even numbers)= series for problem 2 ( the odd numbers). So (pi^2)/6-(pi^2)/24= (pi^2)/8
and what kind of problems are these called? Thanks so much and sorry for the typo in the beginning! I posted it at like 3 am.