# How to find the sum of the series: [duplicate]

How to find the sum of the series:

$\sum _{n=0}^{\infty}a_nx^n$

where $a_0=0,a_1=1,a_{n+1}=a_{n-1}+a_{n}$

Please give some hints on how to find the sum

Hint. $$f(x)=\sum_{n=0}^\infty a_nx^n = x+ \sum_{n=2}^\infty(a_{n-2}+a_{n-1})x^n = x + x\sum_{n=1}^{\infty}a_nx^n+ x^2\sum_{n=0}^{\infty}a_nx^n = x+xf(x)+x^2f(x)$$

• good idea thanks – Learnmore Jan 3 '15 at 15:57
• @learningmaths, not at all =). – Jihad Jan 3 '15 at 15:58