设s=(√1x2)+(√2x3)+(√3x4)+...+(√n(n+1)),求证n(n+1)/2
问题描述：
设s=(√1x2)+(√2x3)+(√3x4)+...+(√n(n+1)),求证n(n+1)/2
答
s=(√1x2)+(√2x3)+(√3x4)+...+(√n(n+1)),√1x2＞1,√2x3＞2,√3x4＞3┄┄√n(n+1)＞n,s=(√1x2)+(√2x3)+(√3x4)+...+(√n(n+1))＞1+2+3┄┄+n=n(n+1)/2；(1+2)/2＞√(1×2),(2+3)/2＞√(2×3)┄┄(n+n+1)/2＞√[...