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Prove algebraically?
(2n+1)^2 - (2n+1) is an even number
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- stanschimLv 76 years ago
Expanding gives:
4n^2 + 4n + 1 - 2n - 1 = 4n^2 + 2n = 2(n^2 + n).
Two times any number, n^2 + n, is an even number.
- Rita the dogLv 76 years ago
Factor out the common factor, 2n+1:
(2n+1)^2 - (2n+1) = (2n+1) ( (2n+1) - 1 ) = (2n+1)(2n)
which is even since it is 2 times the integer n(2n+1).
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