1*3/1+3*5/1+5*7/1+...+2009*2011/1

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  • /表示分数线时,习惯分子写在前面,分母写在后面

    1/1×3+1/3×5+1/5×7+...+1/2001×2003

    =(1/2)×[2/1×3+2/3×5+2/5×7+...+2/2001×2003]

    =(1/2)×[(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+...+(1/2001-1/2003)]

    =(1/2)×(1-1/3+1/3-1/5+1/5-1/7+...+1/2001-1/2003)

    =(1/2)×(1-1/2003)

    =(1/2)×(2009/2011)

    =1001/2011