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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


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

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

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

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