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.