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1MileCrash
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I think I'm pretty good at standard induction. Never had a problem.
Induction and recursion is mercilessly whooping my ***.
Let a1 = 1. For each natural number n > 1, let an = 3an-1 - 1.
Prove that for each natural number n, an = 1/2(3n-1 + 1)
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?
Induction and recursion is mercilessly whooping my ***.
Homework Statement
Let a1 = 1. For each natural number n > 1, let an = 3an-1 - 1.
Prove that for each natural number n, an = 1/2(3n-1 + 1)
Homework Equations
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?