- #1
PCSL
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I have to find the sum of the power series: [tex]\sum_{n=1}^\infty nx^{n+1}[/tex]
I know the I'm supposed to show work but I don't have any idea where to start. I'm not asking for you to do the problem for me, just a hint.
The only idea I had was to take the derivative to get rid of the n+1 in the exponent but I'm not sure if [tex]\sum_{n=1}^\infty n(n+1)x^{n}[/tex] is any easier to solve.
Also I tried looking at the integral but again didn't see what to do
[tex]\sum_{n=1}^\infty \frac{nx^{n+2}}{n+2}[/tex]
Thank you.
I know the I'm supposed to show work but I don't have any idea where to start. I'm not asking for you to do the problem for me, just a hint.
The only idea I had was to take the derivative to get rid of the n+1 in the exponent but I'm not sure if [tex]\sum_{n=1}^\infty n(n+1)x^{n}[/tex] is any easier to solve.
Also I tried looking at the integral but again didn't see what to do
[tex]\sum_{n=1}^\infty \frac{nx^{n+2}}{n+2}[/tex]
Thank you.