Recursion

Recursion is defining something in terms of a previous term, function, etc. For example, the famous Fibonacci sequence is defined recusively. If we let $F_n$ be the nth term, the sequence is: $\displaystyle F_0=1, F_1=1, F_2=2, F_3=3, F_4=5, F_5=8$ , and so on. A recusive definition is: $F_{n+1}=F_{n}+F_{n-1}$ . That is a symbolic way to say "The next term is the sum of the two previous terms".

Examples

A combinatorical use of recursion: AIME 2006I/11
Use of recursion to compute an explicit formula: AIME 2006I/13

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Recursion

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