(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Homework Help: Converging/Diverging Series

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