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An induction proof of a formula consists of three parts.

a) Show the formula is true for

.
b) Assume the formula is true for

.
c) Using b), show the formula is true for

For c), the usual strategy for a summation

is to manipulate

into the form

Induction is a method for checking a result; discovering the result may be hard.

Contributed by: Ed Pegg Jr

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Proof by Induction