You mean-1<= sin^2(n)<= 1 but the comparison test uses absolute values that doesn't matter.

Except for the unimportant sign error, yes.1/n^2 <= [sin^2(n)]/ n^2 <= 1/n^2

Note: sin^2(n) = [sin(n)]^2

I then compared the series to 1/n^2 and determined that the series 1/n^2 is a harmonic p series, where p > 1 and so it converges. Thus, the series converges.

Could someone tell me if i am doing this correctly

Thanks in advance,

ArTiCk