如何证明(n+1)(1/2)^n,当n大于等于2且n是自然数时,单调递减?

显然(n+1)(1/2)^n>0
令f(x)=(x+1)*(1/2)x
f(n)=(n+1)(1/2)^n
f(n+1)=(n+2)(1/2)^(n+1)
f(n+1)/f(n)=1/2*(n+2)/(n+1)=(n+2)/(2n+2)
f(n+1)/f(n)-1=(n+2)/(2n+2)-1=-n/(2n+2)