证明：(1+1/n)^n=1+C(n,1)(1/n)+C(n,2)(1/n)²+C(n,3)(1/n)³+…+(1/n)^n=1+1+[n(n-1)/2!](1/n)²+[n(n-1)(n-2)/3!](1/n)³+…+(1/n)^n=2+(1/2!)[1-(1/n)]+(1/3!)[1-(1/n)][1-(2/n)]+…+(1/n!)[1-(1/n)][1 展开
证明：(1+1/n)^n=1+C(n,1)(1/n)+C(n,2)(1/n)²+C(n,3)(1/n)³+…+(1/n)^n=1+1+[n(n-1)/2!](1/n)²+[n(n-1)(n-2)/3!](1/n)³+…+(1/n)^n=2+(1/2!)[1-(1/n)]+(1/3!)[1-(1/n)][1-(2/n)]+…+(1/n!)[1-(1/n)][1-(2/n)]…[1-(n-1)/n]＜2+(1/2!)+(1/3!)+…+(1/n!)＜2+(1/1*2)+(1/2*3)+…+[1/n(n-1)]=2+[1-(1/2)]+…+[1/(n-1)-1/n]=3-(1/n)＜3 收起
