Prove $ 2<(1+\frac{1}{n})^{n}$ How to prove that $ 2<(1+\frac{1}{n})^{n}$ for every integer $n>1$. I was thinking by induction, it works for $n=2$ but then I couldn't move forward.

By the Binomial theorem,
$$\left(1+\frac1n\right)^n=1+\binom n1\frac1n+\cdots=1+\frac nn+\cdots$$ where the extra terms are positive.
