Summing Series: 1/(n!*n) and 1/(n!*n^2) | Math Homework Help

[zli034]

Homework Statement

I just trying to sum this series, 1/(n!*n) n from 1 to infinity. also similar 1/(n!*n^2)

Homework Equations

$$\sum\frac{1}{(n!*n)}$$
$$\sum\frac{1}{(n!*n^2)}$$

The Attempt at a Solution

I know$$\sum\frac{1}{n!}=e$$
$$\sum\frac{1}{n}=ln$$

My math technique is rusty, can anyone help? thanks in advance. ciao

 

[Dick]

The sum of 1/n isn't ln. It diverges. And both of those sums involve nasty non-elementary functions. I only know this because I looked them up. Why do you think you have to evaluate them exactly? A numerical approximation to both converges very rapidly.

 

[zli034]

Thanks. I am doing study on statistics. On some topic I have sum up probabilities of infinite number of events. I have done numberical approximation with excel, and the result is equivalent to a specific event. I was trying to show why.