计算(1/2+1/3+...+1/2008)*(1+1/2+...+1/2007)-(1+1/2+...+1/2008)
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计算(1/2+1/3+...+1/2008)*(1+1/2+...+1/2007)-(1+1/2+...+1/2008)*(1/2+1/3+...+1/2007)
求求你们了.回答得好我会追加分的(之所以现在没有是怕没人答啦)谢谢
求求你们了.回答得好我会追加分的(之所以现在没有是怕没人答啦)谢谢
![计算(1/2+1/3+...+1/2008)*(1+1/2+...+1/2007)-(1+1/2+...+1/2008)](/uploads/image/z/7769041-25-1.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%881%2F2%2B1%2F3%2B...%2B1%2F2008%EF%BC%89%2A%EF%BC%881%2B1%2F2%2B...%2B1%2F2007%29-%281%2B1%2F2%2B...%2B1%2F2008%29)
令a=1/2+1/3+...+1/2007
则原式=(a+1/2008)(1+a)-(1+a+1/2008)a
=a(1+a)+1/2008(1+a)-a(1+a)-1/2008a
=1/2008(1+a)-1/2008a
=1/2008+1/2008a-1/2008a
=1/2008
则原式=(a+1/2008)(1+a)-(1+a+1/2008)a
=a(1+a)+1/2008(1+a)-a(1+a)-1/2008a
=1/2008(1+a)-1/2008a
=1/2008+1/2008a-1/2008a
=1/2008