Use comparison test to determine convergence of the following series?

Question

$sum_(n-1)^oo(n+1)/n^2$

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Answer 1 · 2018-03-27T19:35:03

$sum_(n-1)^oo(n+1)/n^2$ is divergence

Let $a_n$ = $(n+1)/n^2$ and $b_n$ = $1/n$ are sequence of positive real numbers.

such that

$L$ = $lim_(n->+∞)((n+1)/n^2)/(1/n)$ = $lim_(n->+∞)((n+1)/n)$ = $1$

Because

$sum_(n-1)^oo(1/n)$ is divergence,

so, by using limit ratio test (comparison test),

we said that $sum_(n-1)^oo(n+1)/n^2$ is divergence.