Does the series ∑n=1∞12n−n\sum_{n=1}^{\infty} \frac{1}{2^n - n}∑n=1∞2n−n1 converge?
Yes, by comparison with ∑1/2n\sum 1/2^n∑1/2n
No, it diverges
Yes, by ratio test
Yes, by root test