0
$\begingroup$

This question already has an answer here:

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

$\endgroup$

marked as duplicate by Omnomnomnom, k170, JimmyK4542, Did sequences-and-series Jan 3 '15 at 16:04

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

2
$\begingroup$

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

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.