Why can't WolframAlpha compute the series$$\sum_{n=1}^{\infty} \frac{\mu(n)}{e^{2n}-1}$$where $\mu$ is the Möbius function? The series is obviously absolutely convergent (summands dominated by $2e^{-2n}$ plus geometric series) and therefore clearly convergent. But WolframAlpha says this series diverges: https://www.wolframalpha.com/input?i=sum+%28Moebius+function%28n%29%29%2F%28e%5E%282n%29-1%29+from+1+to+infty.
By summation up to $N=1000$ (https://www.wolframalpha.com/input?i=sum+%28Moebius+function%28n%29%29%2F%28e%5E%282n%29-1%29+from+1+to+1000) it is
$$\sum_{n=1}^{1000} \frac{\mu(n)}{e^{2n}-1}\\=0.1353352832366126918939994949724844034076315459095758814681588726...\\\approx e^{-2}$$and therefore$$\sum_{n=1}^{\infty} \frac{\mu(n)}{e^{2n}-1}=e^{-2}$$should be the value of the series .