- #1

- 239

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- Homework Statement
- study convergence and absolute convergence

- Relevant Equations
- numerical series

## \sum_{n=1}^\infty (-1)^n \frac {log(n)}{e^n}##

i take the absolute value and consider just

## \frac {log(n)}{e^n}##

i check by computing the limit if the necessary condition for convergence is satisfied

##\lim_{n \rightarrow +\infty} \frac {log(n)}{e^n} =\lim_{n \rightarrow +\infty} \frac {1}{ne^n}=0 ##

condition satisfied, now how do i find the rest? with which function can i compare it in order to find if it absolutely converges or not?

in the sense that, at this point i should find some serie for which i know the behaviour, then through comparison or asymptotic comparison i ca find out if the series converges or not.

i take the absolute value and consider just

## \frac {log(n)}{e^n}##

i check by computing the limit if the necessary condition for convergence is satisfied

##\lim_{n \rightarrow +\infty} \frac {log(n)}{e^n} =\lim_{n \rightarrow +\infty} \frac {1}{ne^n}=0 ##

condition satisfied, now how do i find the rest? with which function can i compare it in order to find if it absolutely converges or not?

in the sense that, at this point i should find some serie for which i know the behaviour, then through comparison or asymptotic comparison i ca find out if the series converges or not.

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