简便计算 5/6+11/12+19/20+29/30+55/56+71/72=5/6+11/12+19/20+29/30+41/42+55/56+71/72
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 18:51:05
![简便计算 5/6+11/12+19/20+29/30+55/56+71/72=5/6+11/12+19/20+29/30+41/42+55/56+71/72](/uploads/image/z/8424-0-4.jpg?t=%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97+5%2F6%2B11%2F12%2B19%2F20%2B29%2F30%2B55%2F56%2B71%2F72%3D5%2F6%2B11%2F12%2B19%2F20%2B29%2F30%2B41%2F42%2B55%2F56%2B71%2F72)
简便计算 5/6+11/12+19/20+29/30+55/56+71/72=5/6+11/12+19/20+29/30+41/42+55/56+71/72
简便计算 5/6+11/12+19/20+29/30+55/56+71/72=
5/6+11/12+19/20+29/30+41/42+55/56+71/72
简便计算 5/6+11/12+19/20+29/30+55/56+71/72=5/6+11/12+19/20+29/30+41/42+55/56+71/72
中间少了个+41/42吧?
5/6+11/12+19/20+29/30+41/42+55/56+71/72
=(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)+(1-1/42)+(1-1/56)+(1-1/72)
=7-(1/6+1/12+1/20+1/30+1/56+1/72)
=7-(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)
=7-(1/2-1/9)
=7-7/18
=6又11/18
原式=(1-1/6)+(1-1/12)+......+(1-1/72)
=6+(1/2-1/3)+(1/3-1/4)+......+(1/8-1/9)
=6+1/2-1/9
=6+7/18
=115/18
祝您愉快
望采纳
5/6+11/12+19/20+29/30+55/56+71/72
=1-1/6+1-1/12+1-1/20+1-1/30+1-1/56+1-1/72
=7×1-(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)
=7-(1/2-1/9)
=7-7/18
=6又11/18