Try induction, it's real easy in this case.

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- Jul 12th 2010, 05:43 PM #1

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- Jul 12th 2010, 06:53 PM #2

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- Jul 12th 2010, 07:40 PM #3

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- Jul 13th 2010, 09:32 AM #4

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- Jul 13th 2010, 10:47 AM #5

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Hello, jess0517!

We can prove it by deriving that function ourselves . . .

. .

We have: .

Let

. . and we have: .

Divide by

. . Then: .

The generating function is of the form: .

We know the first two values of the sequence:

. .

Add [1] and [2]: .

Substitute into [1]: .

Hence: .

Therefore: .

- Jul 14th 2010, 03:29 AM #6