1. ## Limits

Given that $(1+1/n)^n \rightarrow e$ as $n \rightarrow \infty$, show that $(1+1/n)^{n+1} \rightarrow e$ as $n \rightarrow \infty$. Note: May use theorems containing sums, products, or quotients of convergent sequences.

2. Originally Posted by Zocken

Given that $(1+1/n)^n \rightarrow \infty$, show that $(1+1/n)^{n+1} \rightarrow e$ as $n \rightarrow \infty$. Note: May use theorems containing sums, products, or quotients of convergent sequences.
there's something very wrong with this problem! are you sure you wrote the question correctly? (check the problem carefully!)

3. mixed up the first part. fixed now.

4. Originally Posted by Zocken
mixed up the first part. fixed now.
$(1 + 1/n)^{n+1}=(1+1/n)^n (1+1/n)$ and we know $(1+1/n)^n \to e$ and $1 + 1/n \to 1,$ as $n \to \infty.$ so the result follows.