Sum of infinite power series with factorial

Question

I don't know how to start to solve this, can you give me some hints? I can solve it without the factorial, but with the factorial, it creates problems...

Thank you!

score 3 · Accepted Answer · answered Nov 08 '18 at 12:48

3

Write down the Maclaurin series for $xe^x$ and differentiate it wrt $x$.

answered Nov 08 '18 at 12:48

Richard Martin

1,671

Thank you, it helped me resolve it! – netwon1227 Nov 08 '18 at 16:26

score 3 · Answer 2 · answered Nov 08 '18 at 12:56

3

$$\dfrac n{(n-1)!}x^n=x^2\cdot\dfrac{x^{n-2}}{(n-2)!}+x\cdot\dfrac{x^{n-1}}{(n-1)!}$$

$e^y=\sum_{r=0}^\infty\dfrac{y^r}{r!}$

answered Nov 08 '18 at 12:56

lab bhattacharjee

274,582

Sum of infinite power series with factorial

2 Answers2