提示:1/n(n+1) = ((n+1)-n)/(n*(n+1)) = 1/n-1/(n+1)
故 1/n(n+1)+1/(n+1)*(n+2)+1/(n+2)*(n+3)+...+1/(n+99)*(n+100)的
每一项拆开消项,等于 (1/n-1/(n+1))+(1/(n+1)-1/(n+2))+...+(1/(n+99)-1/(n+100)) = 1/n - 1/(n+100)
= 100/(n+100)
提示:1/n(n+1) = ((n+1)-n)/(n*(n+1)) = 1/n-1/(n+1)
故 1/n(n+1)+1/(n+1)*(n+2)+1/(n+2)*(n+3)+...+1/(n+99)*(n+100)的
每一项拆开消项,等于 (1/n-1/(n+1))+(1/(n+1)-1/(n+2))+...+(1/(n+99)-1/(n+100)) = 1/n - 1/(n+100)
= 100/(n+100)