1\x(x+1)+1\(x+1)(x+2)+1\(x+2)(x+3)+----+1\(x+2012)(x+2013)
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1\x(x+1)+1\(x+1)(x+2)+1\(x+2)(x+3)+----+1\(x+2012)(x+2013)1\x(x+1)+1\(x+1)(x+2)+1\(x+2)(x+3)+----+1\
1\x(x+1)+1\(x+1)(x+2)+1\(x+2)(x+3)+----+1\(x+2012)(x+2013)
1\x(x+1)+1\(x+1)(x+2)+1\(x+2)(x+3)+----+1\(x+2012)(x+2013)
1\x(x+1)+1\(x+1)(x+2)+1\(x+2)(x+3)+----+1\(x+2012)(x+2013)
1\x(x+1)+1\(x+1)(x+2)+1\(x+2)(x+3)+----+1\(x+2012)(x+2013)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+.+1/(x+2012)-1/(x+2013)
=1/x-1/(x+2013)
=2013/x(x+2013)
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答：
原式
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+2012)-1/(x+2013)
=1/x-1/(x+2013)
=2013/[x(x+2013)]
1\x(x+1)+1\(x+1)(x+2)+1\(x+2)(x+3)+----+1\(x+2012)(x+2013)
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3).......+1/(x+2012)-1/(x+2013)
=1/x-1/(x+2013)
=2013/x(x+2013)
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