1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+........1/(20x21x22)=?

高手说哈!!

推荐答案 2007-03-26

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.........1/(20*21*22)
=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22]
=1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/20*21-1/21*22]
=1/2[1/2-1/21*22]
=1/2*115/231
=115/462

温馨提示：答案为网友推荐，仅供参考

当前网址：http://88.wendadaohang.com/zd/ggKBKKBa.html

其他回答

第1个回答 2007-03-27

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.........1/(20*21*22)
=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22]
=1/2[1/2-1/21*22]
=1/2*115/231
=115/462

第2个回答 2013-03-25

相似回答

1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=?答：1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.1/(20*21*22) =1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22] =1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/20*21-1/21*22] =1/2[1/2-1/21...

1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.答：1/(2x3x4)=1/2x(1/2+1/4)-1/3 1/(3x4x5)=1/2x(1/3+1/5)-1/4 ...1/(98x99x100)=1/2(1/98+1/100)-1/99 因此可以得到 1/(1x2x3)+ 1/(2x3x4) +1/(3x4x5) +...+ x1/(98x99x100)=1/2x(1+1/2+...+1/98+1/3+1/4+...+1/100)-(1/2+1/3+..+1...

1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+...1/(nx(n+1)x(n+2)=?答：以上所有式子相加，错项相加减得：1/1*2*3+1/2*3*4+...+1/n(n+1)(n+2)=0.5/1-0.5/2-0.5/(n+1)+0.5/(n+2)=1/4-0.5/[(n+1)(n+2)]

求结果 1/(1x2x3)+1/(2x3x4)+1/(3x4x5).1/(99x100x101)=?答：1/(1x2x3)+1/(2x3x4)+1/(3x4x5).1/(99x100x101)=1/2×【1/1×2-1/2×3＋1/2×3-1/3×4＋1/3×4-1/4×5+.+1/99×100-1/100×101】=1/2×（1/2-1/10100）=5049/20200

1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+...1/(20x21x22)=?答：1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+...1/(20*21*22)=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22]=1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/20*21-1/21*22]=1/2[1/2-1/21*...

2.计算1/(1*2*3)+1/(2*3*4)+1/(3*4*5?答：运用公因数，进行通分，然后相加，得到结果。

1×2×1/3+2×3×1/4,加3×4×1/5,加省略号加16×17×1/18?答：应该是:1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+…+1/(16x17x18)=1/2x[1/(1x2)-1/(2x3)+1/(2x3)-1/(3x4)+1/(3x4)-1/(4x5)+…+1/(16x17)-1/(17x18)]=1/2x[1/(1x2)-1/(17x18)]=1/2x[1/2-1/306]=1/2x76/153 =38/153 ...

1/(1X2X3)+1/(2X3X4)+…+1/[n(n+1)(n+2)]<1/4 求证答：n+2)]=1/1x2x3+1/2x3x4+1/3x4x5+...+1x/n(n+1)(n+2)=(1/2)[1/1-2/2+1/3+1/2-2/3+1/4+1/3-2/4+1/5+/4-2/5+1/6 +...+1/n-2/(n+1)+1/(n+2)]=(1/2)[1-1/2-1/(n+1)+1/(n+2)]=(n^2+3n)/[4(n+1)(n+2)] 小于4分之1 ...

大家正在搜

(x1+x2+x3)^2 47x103一47x3 x1+x2+x3平方函数f(x)=x3 x3/1+x2的积分 x1+x2公式 f(x)=x³ f(x)=x² x39和x37