Question

Determine if the following series is convergent or divergent.

sum of ( (sin n) / n)^2 from n = 1 to n = inf

not sure it should be here though... I can't find Calculus 2 room. Thanks.

Answer 1

Easier look of this problem :

\[\sum_{n = 1}^{\infty} \ (\frac{ \sin n }{ n }) ^ {2}\]

Answer 2

I thought I was in a wormhole to the past, but then I realized I was in a wormhole to the past.

Answer 3

lol .... I also think the answer is converge (to zero) as same as yesterday one ..... but I don't know how to prove it.

Answer 4

DAMNIT .... Got it.... because

\[\sum_{n = 1}^{\infty} (\frac{ \sin n }{ n }) ^{2} \le \sum_{n = 1}^{\infty} (\frac{ 1 }{ n }) ^{2}\]

for every n because

\[0 \le \sin n \le 1\]

for every n

and the second series converge because it is p-serie. so the first series converge.

Thank you sir !!!!