3/2-5/6+7/12-9/20+11/30-13/42+15/56求解答

3/2-5/6+7/12-9/20+11/30-13/42+15/56求解答
3/2-5/6+7/12-9/20+11/30-13/42+15/56求解答

3/2-5/6+7/12-9/20+11/30-13/42+15/56求解答
=(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/-1/6-1/7+1/7+1/8
=1+1/8
=9/8

3/2=1+1/2
5/6=1/2+1/3
7/12=1/3+1/4
9/20=1/4+1/5
11/30=1/5+1/6
13/42=1/6+1/7
15/56=1/7+1/8
所以
3/2-5/6+7/12-9/20+11/30-13/42+15/56
=(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