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

1/6+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/...

全部展开

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~

收起