calculus - What is the limit of the sequence $(frac{3-4n}{1+n})(1+frac1n)^n$?

I am trying to find the limit of the sequence

$$\left(\frac{3-4n}{1+n}\right)\left(1+\frac1n\right)^n$$
I am aware that if one sequence converges and another sequence converges then the multiplication of two sequences also converge. The limit of the first sequence is $-4$. However I do not know how to calculate the limit of the second sequence.

Answer

Here is one approach

$$\left( 1+\frac{1}{n}\right)^{n}=e^{ n \ln(1+\frac{1}{n}) } = e^{ n (\frac{1}{n}-\frac{1}{2 n^2}+\dots) } = e^{1-\frac{1}{2n}+\dots}\underset{\infty}{\longrightarrow} e$$