Does ∑n=1∞12n+1\sum_{n=1}^{\infty} \frac{1}{2^n+1}∑n=1∞2n+11 converge?
Yes, by comparison with ∑12n\sum \frac{1}{2^n}∑2n1.
No, because the denominator is larger than 2n2^n2n.
Yes, by the Divergence Test.
No, by comparison with ∑1n\sum \frac{1}{n}∑n1.