un=sin 1/n ->0

Let f (x) = sin1/x.

f'(x)=cos 1/x (- 1/x？ )& lt0

therefore

Un is a decreasing sequence.

therefore

Through Leibniz discriminant method, we get

Convergence of series.

∑sin 1/n series

lim(n->； ∞)(sin 1/n)/( 1/n)= 1

And ∑ 1/n score.

That is ∑sin 1/n divergence.

therefore

Series is conditionally convergent.