How to compute this limit which seems to be e?

Question

Compute :$$\lim_{n\to\infty} \Bigg(1+\ln\frac{n+1}{n}\Bigg)^n$$

Answer 1

Idea: Can you establish and then use that $$\frac{1}{n+1}\;<\;\ln\frac{n+1}{n}\;<\;\frac 1n\;\;?$$