SOLUTION: for each series, determine if the series converges or diverges. list at least the first 5 partial sums for each series. if the series converges, state the value. show graphical sup

Question 417410: for each series, determine if the series converges or diverges. list at least the first 5 partial sums for each series. if the series converges, state the value. show graphical support for you conclusions.
infinite above sigma, k=1 under sigma, (1/(k-1!) on the side
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
I think you're implying the sum .

We can use the ratio test. We wish to show that

exists and is less than 1. This limit is equal to

Hence, the series converges. If you know the Taylor series and that the sums and are equivalent when x=1, we conclude that the series converges to .
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