Posted by sarah on Tuesday, February 26, 2008 at 11:08pm.
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
High-order 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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