1. The problem statement, all variables and given/known data Does the series ∑[n=1,∞) sin4n / 4^n converge or diverge? 2. Relevant equations Ratio Test lim n->∞ | a_n+1 / a_n | 3. The attempt at a solution By Ratio Test. Let a_n = sin(4n) / 4^n So, lim n->∞ | (sin (4n+1) / 4^n+1) / (sin 4n / 4^n) | Skipping a few steps.. = | (sin(4n+1)/sin(4n)) * (4^n)/(4^n * 4^1) | = 1/4 * lim n->∞ (sin(4n+1)/sin(4n)) Here's my problem. How do I take the limit of (sin(4n+1)/sin(4n))? Did I do the whole problem wrong? Should I have used Root test?