I think I'm pretty good at standard induction. Never had a problem.(adsbygoogle = window.adsbygoogle || []).push({});

Induction and recursion is mercilessly whooping my ***.

1. The problem statement, all variables and given/known data

Let a_{1}= 1. For each natural number n > 1, let a_{n}= 3a_{n-1}- 1.

Prove that for each natural number n, a_{n}= 1/2(3^{n-1}+ 1)

2. Relevant equations

3. The attempt at a solution

WAT

I can "build it." And I don't even feel comfortable doing that. Let S be the set of n for which the theorem holds.

Let n = 2

Theorem holds.

Let n = 3

Theorem holds.

So 2,3 are elements of S.

(Do I have to show it for 2? Or more? Or just one? Why?)

Suppose that n >= 3 and {1,2,....,n} is a subset of S.

I have no idea what to do. At all. Can someone please explain recursion induction to me?

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# Induction and Recursion.. I have NO idea!

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