1/4+1/12+1/24+.+1/180
=1/4+(1/4-1/6)+(1/6-1/8)+.+(1/18-1/20)
=1/4+1/4-1/6+1/6-1/8+.+1/18-1/20
=1/4+1/4-1/20
=1/2-1/20
=10/20-1/20
=9/20