- #1
Rossinole
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Homework Statement
Does the series ∑[n=1,∞) sin4n / 4^n converge or diverge?
[h2]Homework Equations[/h2]
Ratio Test
lim n->∞ | a_n+1 / a_n |
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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