1 1 1 1 1 1 1 1 1
— + — + — + — + — + — + — + — +—=?
2 6 12 20 30 42 56 72 90
1 1 1 1 1 1 1 1 1
— + — + — + — + — + — + — + — +—=?
2 6 12 20 30 42 56 72 90
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1-1/10
=9/10
1/2+1/6+1/12+...+1/90
=1/(1*2)+1/(2*3)+1/(3*4)+.....+1/(9*10)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)
=1-1/10=9/10