1/2+1/6+1/12+1/20+……+1/90
=1/2 + 1/2*1/3 + 1/3*1/4 + 1/4*1/5 + .+ 1/9*1/10
=1/2 + 1/2 - 1/3 + 1/3 - 1/4 +1/4-1/5 + ...+ 1/9 - 1/10
= 1-1/10
=0.9