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I see intuitively $\left( 1+\dfrac {1} {n}\right) ^{n}$ is increasing but I think, it is not obvious. How can I prove this?

Recall. If sequence of $\left\{ x_{n}\right\} _{n}$ is increasing then $x_n<x_{n+1}$ for all $n\in\mathbb{N}$.

Note that the limit converges to $e$ (Euler's number).

Thomas Andrews
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    Not said correctly. The limit is $e$. You want a proof that the sequence of approximations is increasing. I suspect there's one on this site somewhere. – Ethan Bolker Aug 14 '17 at 21:20
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    The limit is a number (assuming it exists, which it does); it can't be increasing. The underlying sequence can be. – anomaly Aug 14 '17 at 21:21
  • @anomaly The sequnce is increasing. –  Aug 14 '17 at 21:56

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