# An odd coincidence?

Algebra Level 1

$$1$$ is divisible by $$1$$.
$$1\times2\times3$$ is divisible by $$1+2+3$$.
$$1\times2\times3\times4\times5$$ is divisible by $$1+2+3+4+5$$.
$$1\times2\times3\times4\times5\times6\times7$$ is divisible by $$1+2+3+4+5+6+7$$.

In general, is it true that $$1\times2\times\cdots\times n$$ is divisible by $$1+2+\cdots+n$$ for all odd $$n?$$

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