Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.6 AIME Find the answer

1. If $n$ is a positive integer, then the value of $\frac{\left(1-(-1)^{n+1}\right)\left(n^{2}-1\right)}{2}$ is:

Pick one

Solution

$-1 .(B)$
When $n$ is odd, the expression $=0$ ; when $n$ is even, the original expression is an odd number.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.