I take it you mean (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)= (-1)^n/(n!2^n))

Please do not mix "n" and "N"!

Now, do you know whatinductionis? If so, what have you tried to do and where do you have a problem?

Have you checked that, when n= 1, ?