Here $e_n(x)$ is $n$-th partial sum of the exponential series. I was in the proof for $(1+x/n)^n\to e^x$ as $n\to \infty$. It is shown that $e_n(x)\geq (1+x/n)^n$ using binomial theorem.
According to the instruction I have to prove $\lim_{m\to \infty} (1+x/m)^m \geq e_n(x)$. If we prove this we have $e^x\geq\lim_{m\to \infty} (1+x/m)^m \geq e_n(x)$. So $(1+x/n)^n\to e^x$. But I stuck there. Please anyone help, only using sequence and series techniques.
