(1+1/n)²=(1+1/n)·(1+1/n)＞1+1/n∴√(1+1/n)＜1+1/n又√(1+1/n)＞1∴1＜√(1+1/n)＜1+1/n∵lim(n→∞)1=1lim(n→∞)(1+1/n)=1∴lim(n→∞)√(1+1/n)=1
