I have SUM [ ((-1)^n * n!)/n^n ] from n=1 to +inf . I need to check both absolute and conditional convergence.
Now this is very tricky.. the (-1)^n tells me i need to try with the alternating series test.. Than An= n!/n^n , and lim n->inf An is impossible to find for me.
When i tried with Ratio test for absolute convergence i got 1 as result which tells me nothing .
My question here is: Can i cancel n! , and say the series will converge is the series SUM [ 1/n^n ] from n=1 to +inf is converging too ? The last series can be considered as p-series or a geometric series , and it converges since n will always be positive .
At the end does that tells me that the first series is also absolute convergent .
Yes yes .. i got it now... i hope this is the only "special case" of limits when n->inf that is a bit confusing for noobs in math like me.. Because in any other normal example i`m canceling some of the conditions and than just replace n as inf and calculate the result, like i did in this one. I mean if you dont know that term from past , you will go just str8 forward..