- #1

- 107

- 26

$$\sum_{n=2}^{\infty }\frac{3^n-1}{4^n}\zeta (n+1)=\pi$$

I tried to solve this,as I could not solved I requested to wolfram alpha and told me that this sum is

approximately equal to 2.319125.

https://www.wolframalpha.com/input/?i=sum+2+to+infinity+(3^k-1)/4^k+zeta(k+1)

so i do not know if wolfram alpha is wrong or the book have a mistake and I like to know which is wrong.

i tried some other values and the most proximate to pi is minus gamma, but I not quite shure and wolfram alpha calculation time expired u.u.

so i do not know if this is true

$$\sum_{n=2}^{\infty }\frac{3^n-1}{4^n}\zeta (n-\gamma )\approx \pi $$