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Omni-MATH / For a real number x, let ⌊x⌋ stand for the largest integer that is less than or equal to x. Prove that ⌊((n−1)!)/(n(n+1))⌋ is even for every positive integer n.

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problem

For a real number xx, let ⌊x⌋\lfloor x\rfloor stand for the largest integer that is less than or equal to xx. Prove that ⌊(n−1)!n(n+1)⌋\left\lfloor\frac{(n-1)!}{n(n+1)}\right\rfloor is even for every positive integer nn.
Plain-text mathematical notation (without MathML)
For a real number x, let ⌊x⌋ stand for the largest integer that is less than or equal to x. Prove that ⌊((n−1)!)/(n(n+1))⌋ is even for every positive integer n.
Original LaTeX notation
For a real number $x$, let $\lfloor x\rfloor$ stand for the largest integer that is less than or equal to $x$. Prove that $$\left\lfloor\frac{(n-1)!}{n(n+1)}\right\rfloor$$ is even for every positive integer $n$.

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Source and history

task_id
04f201b9-a953-533e-ae51-f44761e7ab61
task_key
test--04f201b9-a953-533e-ae51-f44761e7ab61
task_revision_id
1
config / split
/ test

Official source

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