Question

帮忙解一下两道奥数题(过程）

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

5/6-7/12+9/20-11/30+13/42-15/56+17/72

Answer 1

第一道是很正宗的拆分计算题
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
= 9/8
第二道也是很正宗的....
同理：
5/6-7/12+9/20-11/30+13/42-15/56+17/72
=1/2+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8+1/8+1/9
=1/2+1/9
=11/18
方法是每一个分数可以拆成两个，然后可以消去中间的数简化算式
不懂可以问我~希望对你有帮助~

Answer 2

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
=9/8
(1/2+1/3)-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)+(1/8+1/9)
=1/2+1/9
=11/18

Answer 3

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

Answer 4

裂项即可简算：5/6=1/2+1/3；7/12=1/3+1/4……
原式=3/2-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8
=1又8分之1
同理第二道也可简算：
原式=1/2+1/3-1/3-1/4+……-1/7-1/8+1/8+1/9
=1/2+1/9
=11/18

Answer 5

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
= 9/8

5/6-7/12+9/20-11/30+13/42-15/56+17/72
=1/2+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8+1/8+1/9
=1/2+1/9
=11/18