Another problem by G.H. Hardy

Algebra Level 4

Define the function \(\phi(n) = \left(1 + \dfrac1n\right)^n \).

For \(n \geq 1 \), which is greater, \(\phi(n) \) or \(\phi(n+1)\)?

Note: A previous version of this problem did not have \(n \geq 1,\) so those who answered "impossible to determine" and "it depends" have been given credit.

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