1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4...请根据以上的规律计算：1/6+1/12+1/20+1/30+1/42

来源：学生作业帮助网 编辑：作业帮 时间：2024/08/15 20:57:20
1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4...请根据以上的规律计算：1/6+1/12+1/20+1/30+1/42
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1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4...请根据以上的规律计算：1/6+1/12+1/20+1/30+1/42
1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4...请根据以上的规律计算：1/6+1/12+1/20+1/30+1/42

1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4...请根据以上的规律计算：1/6+1/12+1/20+1/30+1/42
1/6+1/12+1/20+1/30+1/42
=（1/2-1/3）+（1/3-1/4）+（1/4-1/5）+（1/5-1/6）+（1/6-1/7）
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/2-（1/3-1/3）-（1/4-1/4）-（1/5-1/5）-（1/6-1/6）-1/7
=1/2-0-0-0-0-1/7
=5/14

1/6+1/12+1/20+1/30+1/42
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/2-1/7
=7/14-2/14
=5/14

1/6+1/12+1/20+1/30+1/42
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6+1/7
=(1/2-1/7)
=5/14

1/6+1/12+1/20+1/30+1/42
=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/2-1/7
=5/14

不懂可追问
满意请采纳
谢谢

原式=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/2-1/7
=5/14

1*1/2=? 1+1=2? 1+1=2? 1+1×2=? 2-1=1 2+1+2+6= Sn=1/(2^2-1)+1/(4^2-1)+1/(6^2-1)+.+1/[(2n)^2-1]求和 1+2+1+2+1+2+1+2+1+2+1+2+1+2 =( )*( ) =() 巧算：(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4+1/5+1/6)-(1+1/2+1/3+1/4+1/5+1/6)*(1/2+1/3+1/4+1/5)(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4+1/5+1/6)-(1+1/2+1/3+1/4+1/5+1/6)*(1/2+1/3+1/4+1/5)===== (1-1/2)+(1-1/6)+(1-1/12)+...+(1-1/110)=? 1-1/2+1/3-1/4+1/5-1/6+1/7.-1/50=? 1/2+1/6+1/12+...+1/56=快 1/2+1/6+1/12+1/20= 1+1/2+1/6+1/16=? 1/2+1/6+1/12+…+1/1560=? 1*2*3+1-1+1/6=? 已知1/2=1-1/2,1/6=1/2-1/3,请计算1/2-1/6-1/12-1/20...-1/132 1-1/2+1/3-1/4+1/5-1/6+…+1/15=23*[1/( )+1/( )+1/( )+1/( )]