Comparison Test problem with infinite series

[TheRascalKing]

Homework Statement

I need to use the Comparison Test or the Limit Comparison Test to determine whether or not this series converges:

∑ sin(1/n^2) from 1 to ∞

Homework Equations

Limit Comparison Test: Let {An} and {Bn} be positive sequences. Assume the following limit exists:
L = lim[n→∞] An/Bn
if L>0, then ƩAn converges iff ƩBn converges.
if L = ∞ and ƩAn converges, then ƩBn converges.
if L = 0 and ƩBn converges, then ƩAn converges.

Comparison Test: Assume that there exists M > 0 such that 0 ≤ An ≤ Bn for n ≥ M.
if Ʃ[n=1 to ∞] Bn converges, then Ʃ[n=1 to ∞]An also converges.
if Ʃ[n=1 to ∞] An diverges, then Ʃ[n=1 to ∞]Bn also diverges.

The Attempt at a Solution

I've tried comparing with sin(1/n), sin(n), sin(1/n^3), sin(1/n^4), and a handful of other functions involving sin.

Sorry, I'm new to the comparison test and limit comparison test :/

 

[Dick]

Homework Statement

I need to use the Comparison Test or the Limit Comparison Test to determine whether or not this series converges:

∑ sin(1/n^2) from 1 to ∞

Homework Equations

Limit Comparison Test: Let {An} and {Bn} be positive sequences. Assume the following limit exists:
L = lim[n→∞] An/Bn
if L>0, then ƩAn converges iff ƩBn converges.
if L = ∞ and ƩAn converges, then ƩBn converges.
if L = 0 and ƩBn converges, then ƩAn converges.

Comparison Test: Assume that there exists M > 0 such that 0 ≤ An ≤ Bn for n ≥ M.
if Ʃ[n=1 to ∞] Bn converges, then Ʃ[n=1 to ∞]An also converges.
if Ʃ[n=1 to ∞] An diverges, then Ʃ[n=1 to ∞]Bn also diverges.

The Attempt at a Solution

I've tried comparing with sin(1/n), sin(n), sin(1/n^3), sin(1/n^4), and a handful of other functions involving sin.

Sorry, I'm new to the comparison test and limit comparison test :/

Try comparing with 1/n^2. You know that converges, yes?

 

[TheRascalKing]

Thanks, got it now. I was using the Limit Comparison test wrong >.<