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1/1x2+1/2x3+1/3x4+1/4x5+……1/8x9+1/9x10=?(简便算...

1/1x2=1/1-1/21/2x3=1/2-1/31/9x10=1/9-1/101/1x2+1/2x3+1/3x4+1/4x5+……1/8x9+1/9x10=1-1/10=9/10

1/1x2+1/2x3+1/3x4+1/4x5+……+1/9x10=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)++(1/9-1/10)=1-1/10=9/10

裂项求和法 1/1*2=1/1-1/2,1/2*3=1/2-1/3 原式=1/1-1/2+1/2-1/3+1/3-1/4++1/9-1/10=1-1/10=9/10

1/1*2=1-1/21/2*3=1/2-1/31/9*10=1/9-1/10等式两边相加得/1x2+1/2x3+1/3x4+1/4x5+……+1/9x10=1-1/10=9/10

答案是39/40

1/1X2+1/2X3+1/3X4+1/4X5+1/5X6……1/2007X2008=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/2007-1/2008=1-1/2008=2007/2008

1x2/1+2x3/1+3x4/1+4x5/1+23x24/1 =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/23-1/24=1-1/24=23/24

1/1x2+1/2x3+1/3x4+1/4x5+……1/39x40 =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/39-1/40=1-1/40=39/40

1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10 =1-1/2+1/2-1/3+..+1/9-1/10=1-1/10=9/10

请问就这几个,还是以后的也是按这种规律?如果就这几个,那么答案是: 1-1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)=1-1/5=4/5如果后面还有,一直到n的话,答案是: 1-1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+【1/(n-1)-1/n】=1-1/n=(n-1)/n 如果满意.请选为“满意答案”,谢谢.

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