Show that the sum $$ S = \frac{1}{\sqrt{2}}+ \frac{1}{\sqrt{3}} + \dots + \frac{1}{\sqrt{n}} $$ cannot be an integer for any value of $n$. I am completely stumped any help would be welcome.
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3Too many questions begin or end with "I don't even know how to begin with this problem". While this may be true [...], it is still not a valid reason to limit your post to the statement of the problem without any mention of your own thoughts. – From Avoid "no clue" questions. – Martin R Sep 19 '22 at 14:26
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1See e.g. Hagen von Eitzen's solution here – Robert Israel Sep 19 '22 at 14:52