1/2+1/6+1/12+……+1/90
=1/(1*2)+1/(2*3)+...+1/(8*9)+1/(9*10)
=1-1/2+1/2-1/3+...+1/8-1/9+1/9-1/10
=1-1/10
=9/10
1/2+1/6+1/12+…+1/[n*(n+1)]
=1-1/(n+1)