Let \( \mathrm{P}(n) \) be the statement " \( n^{2}+n \) is an even...

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Let \( \mathrm{P}(n) \) be the statement " \( n^{2}+n \) is an even integer". Show that if \( \mathrm{P}(k) \) is true then \( \mathrm{P}(k+1) \) is also true.
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