(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Define an = (a_{n-1}+ a_{n-2})/2 for each positive integer ≥ 2. Use induction to show that: a_{n+1}- a_{n}= (-1/2)^{n}(a_{1}-a_{0})

2. Relevant equations

First show it is true for base case. Assume if it is true for (k), then show it is true for (k + 1).

3. The attempt at a solution

Base case n=1. Then a_{2}- a_{1}= (-1/2)^{1}(a_{1}- a_{0}) = (a_{0}- a_{1})/2

Check: a_{2}- a_{1}= (a_{1}+ a_{0})/2 - a_{1}= (a_{1}+ a_{0}- 2a_{1})/2 = (a0 - a1)/2.

So then do I assume that a_{k+1}- a_{k}= (-1/2)^{k}(a_{1}- a_{0})? Then what?

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

2. Relevant equations

3. The attempt at a solution

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# Use induction to show that

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