1/6+1/12+1/20+1/30+1/42+1/56 简便计算
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/03 04:26:17
![1/6+1/12+1/20+1/30+1/42+1/56 简便计算](/uploads/image/z/8563748-68-8.jpg?t=1%2F6%2B1%2F12%2B1%2F20%2B1%2F30%2B1%2F42%2B1%2F56+%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97)
1/6+1/12+1/20+1/30+1/42+1/56 简便计算
1/6+1/12+1/20+1/30+1/42+1/56 简便计算
1/6+1/12+1/20+1/30+1/42+1/56 简便计算
1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8=1/2-1/8=3/8
1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6+1/7-1/8=1/2-1/8=3/8
观察规律:1/6=1/(2*3)=1/2-1/3,1/12=1/(3*4)=1/3-1/4,1/20=1/(4*5)=1/4-1/5,……
1/56=1/(7*8)=1/7-1/8,所以:
1/6+1/12+1/20+1/30+1/42+1/56
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/7-1/8)
=1/2-1/3+1/3-1/...
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观察规律:1/6=1/(2*3)=1/2-1/3,1/12=1/(3*4)=1/3-1/4,1/20=1/(4*5)=1/4-1/5,……
1/56=1/(7*8)=1/7-1/8,所以:
1/6+1/12+1/20+1/30+1/42+1/56
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/7-1/8)
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/7-1/8
中间抵消后,只剩下头和尾:
原式=1/2-1/8
=4/8-1/8
=3/8
希望对你有帮助哦,亲~
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