计算:x(x+1)分之1(x+1)(x+2)分之1+...(x+2012)(x+2013)分之1

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计算:x(x+1)分之1(x+1)(x+2)分之1+...(x+2012)(x+2013)分之1

x(x+1)分之1+(x+1)(x+2)分之1+...(x+2012)(x+2013)分之1
=1/x-1/(x+1)+1/(x+1)-1/(x-2)+.+1/(x+2012)-1/(x+2013)
=1/x-1/(x+2013)
=(x+2013)/x(x+2013)-x/x(x+2013)
=2013/x(x+2013)

x(x+1)分之1+(x+1)(x+2)分之1+... (x+2012)(x+2013)分之1
=1/x-1/(x+1)+1/(x+1)-1/(x-2)+....+1/(x+2012)-1/(x+2013)
=1/x-1/(x+2013)
=(x+2013)/x(x+2013)-x/x(x+2013)
=2013/x(x+2013)