3/2+7/6+13/12+21/20+31/30+43/42是多少
来源:百度知道 编辑:UC知道 时间:2024/06/07 08:06:13
3/2+7/6+13/12+21/20+31/30+43/42
=1+1/2+1+1/6+1+1/12+1+1/20+1+1/30+1+/42
=6+1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=7-1/7
=48/7
=6又6/7
2、6、12、20、30、42的最小公倍数为420
3/2+7/6+13/12+21/20+31/30+43/42
=1+1/2+1+1/6+1+1/12+1+1/20+1+1/30+1+1/42
=6+210/420+70/420+35/420+21/420+14/420+10/420
=6+360/420
=6+6/7
=6又6/7
或
3/2+7/6+13/12+21/20+31/30+43/42
=1+1/2+1+1/6+1+1/12+1+1/20+1+1/30+1+/42
=6+1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=7-1/7
=6又6/7
3/2+7/6+13/12+21/20+31/30+43/42
=1+1/2+1+1/6+1+1/12+1+1/20+1+1/30+1+1/42
=6+1/2+1/6+1/12+1/20+1/30+1/42
=6+(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)
+(1/5-1/6)+(1/6-1/7)
=6+1-1/7
=6+6/7
=48/7
原式
=1又1/2+1又1/6+1又1/12+1又1/20+1又1/30+1又1/42
=1+1+1+1+1+1+ 1/2+1/6+1/12+1/20+1/30+1/42
=5+1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=5+1-1/7
=6+6/7
=6又6/7
6+1/2