# Power series

• July 18th 2014, 11:07 AM
Haytham1111
Power series
Hello, a question

Show by induction that if
(N +1) an_ +1 + a_n-1 = 0 for all odd numbers n +1 ≥ 2 and a_0 = 1, then a_2N = (((-1) ^n))*((1/((2^n)*n!))
• July 18th 2014, 11:40 AM
HallsofIvy
Re: Power series
I take it you mean $(n+1)a_{n+1}+ a_{n-1}= 0$ (If you don't want to use Latex, use parentheses: (n+1)a_(n+1)+ a_(n-1)= 0.
And I think you mean $a_{2n}= \frac{(-1)^n}{n!2^n}$
(a_(2n)= (-1)^n/(n!2^n))
Please do not mix "n" and "N"!

Now, do you know what induction is? If so, what have you tried to do and where do you have a problem?
Have you checked that, when n= 1, $a_2= 1/2$?
• July 18th 2014, 01:28 PM
Haytham1111
Re: Power series
Ja, i will try to use parentes, because i do not know how to use Latex

The question is to proof by induction that the first stammene is correctly which os equal zero?