1/8=1/(2*4)=1/2*(1/2-1/4)
1/15=1/(3*5)=1/2*(1/3-1/5)
1/24=1/(4*6)=1/2*(1/4-1/6)
......
1/323=1/(17*19)=1/2*(1/17-1/19)
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本回答被提问者采纳
1\/3+1\/8+1\/15+1\/24+...+1\/360=
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 ...
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*(1...
3分之1+8分之1+15分之1+24分之1+...+360分之1+399分之1=
原式=1\/(1×3)+1\/(2×4)+1\/(3×5)+1\/(4×6)+...+1\/(18×20)+1\/(19×21)=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［1+1\/2-1\/20-1\/21］=1\/2×589\/420 =589\/840。
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?_百 ...
思路：分数裂项，前后相抵 答案29\/40 过程附图
1+3又1\/8+5又1\/24+7又1\/48+9又1\/80+11又1\/120+13又1\/168+15又1\/224+1...
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\/2+1\/3+1\/4+1\/5+1\/6+1\/7+1\/8+1\/9+1\/10+...1\/100这道题怎样简算_百度知 ...
没有，这是调和数列，很早就有数学家研究，比如中世纪后期的数学家Oresme在1360年就证明了这个级数是发散的。他的方法很简单： 1 +1\/2+1\/3 +1\/4 + 1\/5+ 1\/6+1\/7+1\/8 +... 1\/2+1\/2+(1\/4+1\/4)+(1\/8+1\/8+1\/8+1\/8)+... 注意后一个级数每一项对应的分数都小于调和级数...
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
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 ...
一个数的分数加上另一个数的分数,和是多少
1+1\/2+1\/3+1\/4+1\/5+1\/6+1\/7+1\/8+1\/9+1\/10 =1+(1\/2+1\/3+1\/6)+(1\/4+1\/5+1\/10)+1\/7+1\/8+1\/9 =1+1+11\/20+1\/8+1\/7+1\/9 =1+1+27\/40+1\/9+1\/7 =1+1+283\/360+1\/7 =1+1+2341\/2520 =1+4861\/2520 ≈2.92896 ...
