- #1
Repetit
- 128
- 2
Hey!
Can someone tell me or just give a hint on how to show that:
[tex]\sum_n \frac{n^2 a^n}{n!}=a(1+a)e^a[/tex]
when n goes to infinity? I know how to show that:
[tex]\sum_n \frac{n a^n}{n!}=a e^a[/tex]
by using the facts that n/n! = 1/(n-1)! and a^n = a a^(n-1). But how can I prove the other one?
Thanks!
Can someone tell me or just give a hint on how to show that:
[tex]\sum_n \frac{n^2 a^n}{n!}=a(1+a)e^a[/tex]
when n goes to infinity? I know how to show that:
[tex]\sum_n \frac{n a^n}{n!}=a e^a[/tex]
by using the facts that n/n! = 1/(n-1)! and a^n = a a^(n-1). But how can I prove the other one?
Thanks!