$\sum_{n=0}^{\infty}\dfrac{1}{2^n-1}$ ve $\sum_{n=0}^{\infty}\dfrac{1}{2^n+1}$

[ArtOfMathSolving]

$\begin{align*}\sum_{n=0}^{\infty}\dfrac{1}{2^n-1}\end{align*}$ ve $\begin{align*}\sum_{n=0}^{\infty}\dfrac{1}{2^n+1}\end{align*}$ ifadelerinin değerini hesaplayınız.