some short and selected math problems of different levels in random order I try to keep the ans simple
we have
(1+ \frac{1}{x})^{x+1} = (\frac{x+1}{x})^{x+1}
=(\frac{x}{x+1})^{-(x+1)}
=(1- \frac{1}{x+1})^{-(x+1)}
= (1+ \frac{1}{-(x+1)})^{-(x+1)}
comparing with the RHS we get -(x+1) = n or x = -(n+1)
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