如何证明Xn=(1+1/n)^n+1是递减数列?

如何证明Xn=(1+1/n)^n+1是递减数列?
如何证明Xn=(1+1/n)^n+1是递减数列?

如何证明Xn=(1+1/n)^n+1是递减数列?
xn/xn+1=((1+1/(n^2+2n))^(n+1))((n+1)/(n+2))
由二项式展开
上式>(1+(n+1)/(n^2+2n))(n+1)/(n+2)=(n^3+4n^2+4n+1)/(n^3+4n^2+4n)>1
递减