To determine the convergence of _ n=1 ^ 2n^ 4 +n^ 2 5n^ 5 -7

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

To determine the convergence of

\sum_{n=1}^{\infty}\frac{2n^{4}+n^{2}}{5n^{5}-7},

which of the following benchmark series would be most appropriate to use? (a)

\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^{4}}

(b)

\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^{2}}

(c)

\displaystyle \sum_{n=1}^{\infty}\frac{1}{n}

(d)

\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^{3/2}}