MathDB

Euler-like limit

Source:

December 13, 2019

real analysislimitsseuqence

Problem Statement

Let be the sequence

\left( a_n \right)_{n\ge 0}

of positive real numbers defined by a_n=1+\frac{a_{n-1}}{n} , \forall n\ge 1. Calculate

\lim_{n\to\infty } a_n ^n .

Florian Dumitrel