Question

series of sin(n)/n converges or diverges?

Answer 1

it converges

Answer 2

by doing what test:O?

Answer 3

i dun remember this stuff anymore

Answer 4

clearly

Answer 5

so how do you know it converges?

Answer 6

i think it does not too sure

Answer 7

it converges by the integral test.
To easily do the integral, note the sine integral function:
\[Si(z)=\int\limits_0^z \frac{sin(t)}{t}dt\]
using that you can do a simple substitution integral and the integral will converge to
0.5(pi-Si(1))

Answer 8

0.5(pi-2Si(1))

actually.