Posted by sarah on Tuesday, February 26, 2008 at 11:08pm.
determine whether the series converges of diverges
the sum from k=1 to infinity of
sin(e^k)
I'm not sure where to start..

calculus  drwls, Wednesday, February 27, 2008 at 3:06am
As k becomes large, e^k becomes much less than 1, and sin(e^k) approaches e^k
The sum of the series 1 + 1/e + 1/e^2 converges to
1 /(1  1/e)= 1.582
Highorder terms of the series
sin(e^k) will behave similarly, but the sum of the entire series will be somethat less than 1.582.
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