1/2² +1/3²+...+1/100²
<1/(1×2)+1/(2×3)+...+1/(99×100)
=(1-1/2) +(1/2 -1/3) +...+(1/99 -1/100)
=1-1/100=99/100
所以
1/2² +1/3²+...+1/100²<99/100