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1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+2007)(xx+2008)
题目详情
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+2007)(xx+2008)
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答案和解析
最后一个应该是(X+2008)吧……
1/x(x+1)=1/x-1/(x+1)
以此类推,原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)……-1/(x+2007)+1/(x+2007)-1/(x+2008)
=1/x-1/(x+2008)
=2008/x(x+2008)
1/x(x+1)=1/x-1/(x+1)
以此类推,原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)……-1/(x+2007)+1/(x+2007)-1/(x+2008)
=1/x-1/(x+2008)
=2008/x(x+2008)
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