Question

试证:对任意的正整数n，有1/(1*2*3）+1/(2*3*4)+……+1/n(n+1)(n+2)<1/4

Answer 1

1/n(n+1)(n+2)=0.5
(
(1/n-1/(n+1))
-(1/(n+1)-1/(n+2))),结果式子是0.5
（
n/(n+1)+1/(n+2)-0.5
）,趋于无穷值为0.25，所以。。n是存在的正整数，所以等式成立。