Question

determine convergence of series= sin^n(1/n) n=1

Answer 1

converges for sure
you do mean the sum right?

Answer 2

yes

Answer 3

then since \(\sin(x)<1\) you can compare it to any geometric series

Answer 4

at least for some rather small value of \(n\) you know \(\sin(\frac{1}{n})<1\) to be more precise

Answer 5

so you just use the comparison test?