Let . To investigate the convergence of , the function will be integrated on . What…

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

Problem

Let

f(x)=\dfrac{x}{x^{3}+1}

. To investigate the convergence of

\displaystyle \sum_{n=1}^{\infty} \dfrac{n}{n^{3}+1}

, the function

f

will be integrated on

[N,\infty)

. What is the least integer

N

for which this strategy meets the necessary hypotheses? (a)

N=2

(b)

N=4

(c)

N=1

(d)

N=0