1又1/2-2又5/6+3又1/12-4又19/20+5又1/30-6又41/42

1又1/2-2又5/6+3又1/12-4又19/20+5又1/30-6又41/42
1又1/2-2又5/6+3又1/12-4又19/20+5又1/30-6又41/42

1又1/2-2又5/6+3又1/12-4又19/20+5又1/30-6又41/42
=1+1/2-3+1/6+3+1/12-5+1/20+5+1/30-7+1/42
=-6+(1/2+1/6+1/12+1/20+1/30+1/42)
=-6+[1/(1*2)+1/(2*3)+1/(3*4)+...+1/(6*7)]
=-6+[(1/1-1/2)+(1/2-1/3)+...+(1/6-1/7)]
=-6+(1-1/7)
=-5又1/7