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