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!))
I take it you mean $\displaystyle (n+1)a_{n+1}+ a_{n-1}= 0$ (If you don't want to use Latex, use parentheses: (n+1)a_(n+1)+ a_(n-1)= 0.
And I think you mean $\displaystyle a_{2n}= \frac{(-1)^n}{n!2^n}$
(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, $\displaystyle a_2= 1/2$?