Problem 341 (difficulty: 4/10)
Calculate the limit of the sequence
\(\displaystyle a_n=\left(\frac{n+2}{n+1}\right)^n .\)
Solution:
\(\displaystyle a_n\left(1+\frac{1}{n+1}\right)=\left(1+\frac{1}{n+1}\right)^{n+1}\to e, \)
therefore \(\displaystyle a_n\to e\).