Question

What is the limit of the function (1+x\n)^n as n tends to infinity?

Answer 1

Answer:

down vote

accepted

A short proof:

(1+xn)n=enlog(1+xn)

Since log(1+x)=x+O(x2) when x→0, we have nlog(1+xn)=x+O(x2n) when n→+∞