How do I show that for every x>0 on has (1+x)^(1/x)<e I proved that e is the limit of the equation, but I don't know how to prove it is strictly less than. e being defined as the limit as x tends to infinity of (1+1/x)^x.
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If is strictly decreasing on and approaches as , then it must be less than for . So I think showing that for should suffice.
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