Question

1/X-1/X(X+1)-1/(X+1)(X+2)-......-1/(X+2013)(X+2014)

求高人解答啊.......急急急！！！

Answer 1

原式=1/X-[1/X(X+1)+1/(X+1)(X+2)+......+1/(X+2013)(X+2014)]
=1/X-[1/X-1/(X+1)+1/(X+1)-1/(X+2)+......+1/(X+2013)-1/(X+2014)]
=1/X-[1/X-1/(X+2014)]
=1/X-1/X+1/(X+2014)

=1/(X+2014)

追问

第三步没看懂 求详细 谢谢

追答

中间的正负抵消

Answer 2

原式=1/x-(1/x-1/(x+1))-(1/(x+1)-1/(x+2))-……-(1/(x+2013)-1/(x+2014))
=1/x-1/x+1/(x+1)-1/(x+1)+1/(x+2)-……+1/(x+2013)-1/(x+2013)+1/(x+2014)
=1/(x+2014)