roles) || in_array('administrator', $user->roles) || in_array('admin', $user->roles ) ) { ?>
probname); ?>
Topic Classification: nid, "Topic Classification"); ?> Tags: nid, "Problem Tag");?>
Topics: nid, "Topics"); ?> Prerequisites: nid, "Prerequisites"); ?>
Supplies: nid, "Supplies"); ?> Pedagogy: nid, "Pedagogy"); ?>
Grade Vs Difficulty:
  EasyModerateChallengingPerplexing
1-2
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5-6
7-8
 
9-10
11-12
13-14
Solution: nid, "Solution"); ?>
Problem

The $\textit{Fibonacci sequence}$ $\left( f_n \right)_{ n \ge 0 }$ is given by the recursion \[ f_0 = 0 , \ f_1 = 1 , \ f_{ n+2 } = f_{ n+1 } + f_n \ \text{ for } n \ge 0 \, . \] Show that \[ F(x) := \sum_{ n \ge 0 } f_n \, x^n = \frac{ x }{ 1 - x - x^2 } \] and use this to derive a closed form for $f_n$.

Details
Authors
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References
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Reference Author Reference Title Reference URL
'; } ?>
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Problem Sets This Problem Belongs to:
parent_nid; ?> Set:
VARIABLES
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DEFINITIONS
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