计算,1x1/3-7/12+9/20-11/30+13/40-15/56=?,1/4+1/28+1/70+1/130+1

1+ 1/3-7/12+9/20-11/30+13/40-15/56
= 1 + 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

原式=1/(1×4)+1/(4×7)+1/(7×10)+1/(10×13)+1/(13×16)
=1/3×(1/1-1/4+1/4-1/.7+1/7-1/10+1/10-1/13+1/13-1/16)
=1/3×(1-1/16)
=1/3×15/16
=5/16