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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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