For which positive values on a does the series converge?:
$ \sum _{n=1}^{\infty}na^{\ln(n)}$
I have tried to rewrite the expression, but that gives me nothing.
Anyone got a clue?
For which positive values on a does the series converge?:
$ \sum _{n=1}^{\infty}na^{\ln(n)}$
I have tried to rewrite the expression, but that gives me nothing.
Anyone got a clue?
I will guess that your $i$ should be an $n$. If $a$ is positive, we may write it as $e^x$ for some $x$. Then $ na^{\ln(n)}=n(e^x)^{\ln(n)}=ne^{\ln(n^x)}=n(n^x)=n^{x+1}. $ Now you've got yourself a $p$-series.
Hint: Use the root test and see what you get.