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Possible Duplicate:
Solving a Recurrence Relation/Equation, is there more than 1 way to solve this?

How do I find an explicit formula for $a_n$ given $a_0 = 3$ and $a_{n+1} = 2a_n + 1$. I'm guessing it's probably related to the formula for first $n$ terms of a geometric series. Any help is appreciated

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    Duplicated: http://math.stackexchange.com/q/106036/238752012-06-04

2 Answers 2

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Write out the first few terms. Add one to each term. Make a conjecture. Prove it by induction.

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Note that $a_{n+1}+1=2a_n+2=2(a_n+1)$. Define then $u_n=a_{n}+1$. Note that $u_{n+1}=2u_n$.