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

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The discussion centers on summing the series 1/(n!*n) and 1/(n!*n^2) from n=1 to infinity. It is established that the sum of 1/n diverges, while the sums in question involve complex non-elementary functions. Numerical approximations for both series converge rapidly, providing practical solutions without requiring exact evaluations. The user seeks assistance due to a lack of familiarity with these mathematical concepts.

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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



[tex]\sum\frac{1}{(n!*n)}[/tex]
[tex]\sum\frac{1}{(n!*n^2)}[/tex]

The Attempt at a Solution


I know[tex]\sum\frac{1}{n!}=e[/tex]
[tex]\sum\frac{1}{n}=ln[/tex]

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

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