1/3=1/(1*3)=1/2*(1-1/3)
1/8=1/(2*4)=1/2*(1/2-1/4)
1/15=1/(3*5)=1/2*(1/3-1/5)
......
1/360=1/(18*20)=1/2*(1/18-1/20)
1/3+1/8+1/15+1/24+...+1/360
=1/2*[(1-1/3)+(1/2-1/4)+(1/3-1/5)+...+(1/17-1/19)+(1/18-1/20)]
=1/2*(1+1/2-1/3+1/3-1/4+...-1/17+1/17-1/18+1/18-1/19-1/20)
=1/2*(1+1/2-1/19-1/20)
=1/2*531/380
=531/760
1\/3+8\/1+1\/15+...+1\/360等于多少
1\/3+1\/8+1\/15+1\/24+...+1\/360 =1\/2*[(1-1\/3)+(1\/2-1\/4)+(1\/3-1\/5)+...+(1\/17-1\/19)+(1\/18-1\/20)]=1\/2*(1+1\/2-1\/3+1\/3-1\/4+...-1\/17+1\/17-1\/18+1\/18-1\/19-1\/20)=1\/2*(1+1\/2-1\/19-1\/20)=1\/2*531\/380 =531\/760 ...
1\/3+1\/8+1\/15+1\/24+...+1\/360=
1\/360=1\/(18*20)=1\/2*(1\/18-1\/20)1\/3+1\/8+1\/15+1\/24+...+1\/360 =1\/2*[(1-1\/3)+(1\/2-1\/4)+(1\/3-1\/5)+...+(1\/17-1\/19)+(1\/18-1\/20)]=1\/2*(1+1\/2-1\/3+1\/3-1\/4+...-1\/17+1\/17-1\/18+1\/18-1\/19-1\/20)=1\/2*(1+1\/2-1\/19-1\/20)...
奥数题1除以3加1除以8加1除以15加1除以24加1除以35加1除以48加1除以63...
=1\/3+1\/8+1\/15+1\/24+1\/35+...+1\/【(n+1)²-1】+...+1\/399 =1\/2*(1-1\/3)+1\/2*(1\/2-1\/4)+1\/2*(1\/3-1\/5)+1\/2*(1\/4-1\/6)+...1\/2*(1\/19-1\/21)=1\/2*(1-1\/3+1\/2-1\/4+1\/3-1\/5+1\/4-1\/6+...+1\/18-1\/20+1\/19-1\/21)=1\/2*(...
3分之1+8分之1+15分之1+24分之1+...+360分之1+399分之1=
=589\/840。
1\/8+1\/24+1\/48+1\/80+...+1\/360的答案是多少
1\/8+1\/24+1\/48+1\/80+...+1\/360 1\/(2x4)+1\/(4x6)+1\/(6x8)+…+1\/(18x20)=(1\/2)x[2\/(2x4)+2\/(4x6)+2\/(6x8)+…+2\/(18x20)]=(1\/2)x(1\/2-1\/4+1\/4-1\/6+1\/6-1\/8+…+1\/18-1\/20)=(1\/2)x(1\/2-1\/20)=9\/40 ...
1\/2+1\/8+1\/24+1\/48+1\/80+1\/120加省略号最后是1\/360这道题目怎么做?
思路：分数裂项，前后相抵 答案29\/40 过程附图
1加3又1\/8+5又1\/24+7又1\/48+9又1 \/80+...19又1\/360等于多少谢谢了,大 ...
原式=(1+3+……+19)+(1\/8+1\/24+1\/48+……+1\/360) =10x(1+19)\/2+1\/4x[(1-1\/2)+(1\/2-1\/3)+……+(1\/9-1\/10)] =100+1\/4x(1-1\/10) =100+9\/40 =100又9\/40 求采纳
...+9又1\/80+11又1\/120+13又1\/168+15又1\/224+17又1\/288+19又1\/360...
1\/8=1\/2[1\/2-1\/4];1\/24=1\/2[1\/4-1\/6]...;1\/360=1\/2[1\/18-1\/20]原式=（1+3+5+。。。+19）+[1\/2*4+1\/4*6+1\/6*8+1\/10*12+1\/12*14+1\/16*18+1\/18*20]=100+1\/2【1\/2-1\/4+1\/4-1\/6+...+1\/18-1\/20】=100+1\/2[1\/2-1\/20]=100+9\/40....
1\/5+1\/30+1\/60+…+1\/360=
n×(n-2)×(n+2)=n3-4n 1×3×5+4×6×8+7×9×11+……+28×30×32 =33-12+63-24+93-36+……+303-120 =(33+63+93+...+303)-(12+24+36+……+120) =33×(13+23+33+...+103)-(12+120)×10÷2 =27×(1+2+3+...+10)2-615 =27×552-615 =27×3025-615 ...
1\/5+1\/30+1\/60+…+1\/360=?求步骤
1\/5+1\/30+1\/60+…+1\/360 =1\/5×（1+1\/6+1\/12+...+1\/72）=1\/5×（1+1\/2-1\/3+1\/3-1\/4+1\/4-1\/5+...+1\/8-1\/9）=1\/5×（3\/2-1\/9）=1\/5×（27\/18-2\/18）=1\/5×25\/18 =5\/18
