## Double An Odd Sum

#### Problem

Consider the following results:

 4 (1) = 1 + 3 4 (1 + 3) = 1 + 3 + 5 + 7 4 (1 + 3 + 5) = 1 + 3 + 5 + 7 + 9 + 11 4 (1 + 3 + 5 + 7) = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15

If $S_n$ represents the sum of the first $n$ odd numbers, prove that $4S_n = S_{2n}$.

Problem ID: 283 (23 Jul 2006)     Difficulty: 2 Star

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