For each of the following series, indicate whether the integral test can be used to determine its convergence or not, and if not, why.

A. $\sum\limits_{n=1}^{\infty} \frac{6}{n^{3}\,(\cos(\pi n) + \sin(\pi n) + 2)}$
Can the integral test be used to test convergence?
A. no, because the terms in the series do not decrease in magnitude
B. no, because the terms in the series are not all positive for $n\ge c$, for some $c>0$
C. no, because the series is not a geometric series
D. no, because the terms in the series are not recursively defined
E. no, because the function $f(x)$ (where $a_n = f(n)$) is not defined for all $x$
F. yes

B. $\sum\limits_{n=1}^{\infty} {n\over n^2 - 5.8}$
Can the integral test be used to test convergence?
A. no, because the terms in the series do not decrease in magnitude
B. no, because the terms in the series are not all positive for $n\ge c$, for some $c>0$
C. no, because the series is not a geometric series
D. no, because the terms in the series are not recursively defined
E. no, because the function $f(x)$ (where $a_n = f(n)$) is not defined for all $x$
F. yes

C. $\sum\limits_{n=1}^{\infty} \frac{\cos(n)}{n^{3}}$
Can the integral test be used to test convergence?
A. no, because the terms in the series do not decrease in magnitude
B. no, because the terms in the series are not all positive for $n\ge c$, for some $c>0$
C. no, because the series is not a geometric series
D. no, because the terms in the series are not recursively defined
E. no, because the function $f(x)$ (where $a_n = f(n)$) is not defined for all $x$
F. yes