Which series diverges by the nnn-th term test (terms do not approach 0)?
∑n=1∞nn+1\sum_{n=1}^{\infty} \frac{n}{n+1}∑n=1∞n+1n
∑n=1∞(−1)n\sum_{n=1}^{\infty} (-1)^n∑n=1∞(−1)n
∑n=1∞cos(nπ)2n\sum_{n=1}^{\infty} \frac{\cos(n\pi)}{2^n}∑n=1∞2ncos(nπ)
∑n=1∞sin(1n)\sum_{n=1}^{\infty} \sin\left(\frac{1}{n}\right)∑n=1∞sin(n1)