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IntroAnalysis
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Homework Statement
Define an = (an-1 + an-2)/2 for each positive integer ≥ 2. Use induction to show that: an+1 - an = (-1/2)n(a1 -a0)
Homework Equations
First show it is true for base case. Assume if it is true for (k), then show it is true for (k + 1).
The Attempt at a Solution
Base case n=1. Then a2 - a1 = (-1/2)1(a1 - a0) = (a0 - a1)/2
Check: a2 - a1 = (a1 + a0)/2 - a1 = (a1 + a0 - 2a1)/2 = (a0 - a1)/2.
So then do I assume that ak+1 - ak = (-1/2)k(a1 - a0)? Then what?