Question

1-6/5+7/12-9/20+11/30-13/42+15/56=?用简便方法计算

Answer 1

5/6=（2+3）/（2*3）=1/2 +1/3
7/12=（3+4）/（3*4）=1/3 +1/4
9/20=（4+5）/（4*5）=1/4+1/5
……
原式=1-1/2-1/3+1/3+1/4-1/4-1/5……+1/7+1/8
=1-1/2+1/8
= 5/8

Answer 2

1-6/5+7/12-9/20+11/30-13/42+15/56
= -1/5 + (1/3 + 1/4) - (1/4+1/5) + (1/5+1/6）- (1/6+1/7) + (1/7+1/8)
= -1/5 + 1/3 + 1/4 - 1/4 - 1/5 + 1/5 + 1/6 - 1/6 - 1/7 + 1/7+1/8
= -1/5 + 1/3 +1/8
= 1/3 +1/8 -1/5
= (40+15-24)/120
= 31/120