1/2+1/6+1/12+1/20+......+1/90怎么转换？

Answer 1

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
=0.9

Answer 2

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