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..
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.