(a) Use the comparison test to carefully determine if $\sum\limits_{n=1}^{\infty} {4^n\over n + 4^n}$ converges or diverges: this series
A. converges
B. diverges

(b) Use the ratio test to carefully determine if $\sum\limits_{n=1}^{\infty} {4^n\over n^3}$ converges or diverges: this series
A. converges
B. diverges

(c) Use the alternating series test to carefully determine if $\sum\limits_{n=1}^{\infty} {(-1)^{n-1}\over \sqrt n + n^3}$ converges or diverges: this series
A. converges
B. diverges

(d) Use the limit comparison test to carefully determine if $\sum\limits_{n=1}^{\infty} {n^3+1\over n^4+4}$ converges or diverges: this series
A. converges
B. diverges