计算1/1X3+1/2X4+1/3X5+.+1/10X12

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计算1/1X3+1/2X4+1/3X5+.+1/10X12
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计算1/1X3+1/2X4+1/3X5+.+1/10X12
计算1/1X3+1/2X4+1/3X5+.+1/10X12

计算1/1X3+1/2X4+1/3X5+.+1/10X12
裂项求和咯
把每一项拆开.1/(N*(N+2))=1/2*(1/N+1/(N+2))
原式=(1/2)X((1-1/3)+(1/2-1/4)+(1/3-1/5)+.+(1/10-1/12))
消去后=(1/2)X(1+1/2-1/11-1/12)=115/132

太难了

楼主啊，这个问题很累，你到底是说1/[n*(n+2)]，还是说1/n*（n+2）?
用极限运算去算吧，书上都有公式。不是很复杂，下次你整个 1/100*102 ，再来。

175/132
1/1X3+1/2X4+1/3X5+......+1/10X12 =
1/2(1-1/3) + 1/2(1/2-1/4) + 1/2(1/3 - 1/5) +.....+1/2(1/10-1/12)
=1/2(1+1/2-1/11-1/12) = 175/132

175/264
1/2(1-1/3+1/2-1/4+1/3-1/5+......+1/10-1/12)==1/2(1+1/2-1/11-1/12)=175/264
其实：是1/2{(n+2)-n}/n(n+2)通项的和

解一道方程组x1+x2+x3=5,x2+x3+x4=1,x3+x4+x5=-5,x4+x5+x1=-3,x5+x1+x2=2 1/1x3+1/2x4+1/3x5+ 1x2+2x3+3x4+4x5+.+15x16 x1-x2+x3=1 x2-x3+x4=2 x3-x4+x5=3 x4-x5+x1=4 x5-x1+x2=5 求x1,x2,x3,x4,x5 简便计算1/2+1/2x3+1/3x4+1/4x5+...+1/99x100 计算1/1X3+1/2X4+1/3X5+.+1/10X12 计算1/1x3+1/2x4+1/3x5+……+1/9x11=? 计算1x2+2x3+3x4+4x5+...+99x100 计算:1x3分之一+2x4分之一+3x5分之一+...+9x11分之一 求解线性方程组 x1-2x2+3x3-x4-x5=2 x1+x2-x3+x4-2x5=1 2x1-求解线性方程组x1-2x2+3x3-x4-x5=2x1+x2-x3+x4-2x5=12x1-x2+x3-2x5=22x1+2x2-5x3+2x4-x5=5 求非齐次线性方程组的通解x1+3x2+5x3-4x4=1x1+3x2+2x3-2x4+x5=-1x1-2x2+x3-x4-x5=3x1+2x2+x3-x4-x5=3 x5-x4+x3-x2+x-1因式分解 X5-X4+X3+X2+X+1因式分解 若x1,x2,x3,x4,x5满足方程组：x1-x2+x3=1 x2-x3+x4=2 x3-x4+x5=3 x4-x5+x1=4 x5-x1+x2=5 求x2,x3,x4的少打了个字，是求x2，x3，x4的值 x1-x2+x3=1x2-x3+x4=21若x1,x2,x3,x4,x5满足方程组 x3-x4+x5=3x4-x5+x1=4x5-x1+x2=5求x2 x3 x4的值2已知 x1+x4+x6+x7=39 x2+x4+x5+x7=49 x3+x5+x6+x7=41 x4+x7=13 x5+x7=14 x6+x7=9 x1+x2+x3+x4+x5+x6+x7=9求x7的值若x1,x2,x3,x4,x5满足方程组 x1-x 求非其次线性方程组 {x1+2x2+x3+x4+x5=1x1+2x2+x3+x4+x5=12x1+4x2+3x3+x4+x5=2-x1-2x2+x3+3x4-x5=5 2x3+4x4-2x5=6 的一般解 计算：1/1x2+1/2x3+1/3x4+1/4x5+……1/39x40 1/1x2+1/2x3+1/3x4+1/4x5...1/2001x2002 简便计算