1/2+1/6+1/12+1/20+1/30+1/42+1/56=?简便运算.
3个回答

1/2+1/6+1/12+1/20+1/30+1/42+1/56

=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)

=(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)

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8

=1-1/8

=7/8