Determine whether this series is a convergent or divergent.

Question

Determine whether this series is a convergent or divergent.

∑ _n=1^∞ 1 /(n + n cos²n)

PLEASE SOLVE THE PROBLEM WITH STEPS

Answer 1

Taha:

We know cos²(n) ≤ 1

So n*cos²(n) ≤ n

n+ncos²(n) ≤ n+n = 2n

So

1/(n+ncos²(n)) ≥ 1/(2n)

What can you say about the series ∑1/(2*n) it's a p-series with p =1. Does it diverge or converge?

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