(a) Check all of the following that are true for the series $\sum\limits_{n=1}^{\infty}\frac{(n - 7)\cos(n\pi)}{n^{2}}$

A. This series converges
B. This series diverges
C. The integral test can be used to determine convergence of this series.
D. The comparison test can be used to determine convergence of this series.
E. The limit comparison test can be used to determine convergence of this series.
F. The ratio test can be used to determine convergence of this series.
G. The alternating series test can be used to determine convergence of this series.

(b) Check all of the following that are true for the series $\sum\limits_{n=1}^{\infty} \frac{7^n}{2^n - 1}$

A. This series converges
B. This series diverges
C. The integral test can be used to determine convergence of this series.
D. The comparison test can be used to determine convergence of this series.
E. The limit comparison test can be used to determine convergence of this series.
F. The ratio test can be used to determine convergence of this series.
G. The alternating series test can be used to determine convergence of this series.