Thực hiện phép tính. 1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+....+1/(x+2013)(x+2014)
Giải thích
1x(x+1)+1(x+1)(x+2)+1(x+2)(x+3)+......+1(x+2013)(x+2014)=1x−1x+1+1x+1−1x+2+1x+2−1x+3+......+1x+2013−1x+2014=1x−1x+2014=2014xx+2014
1x(x+1)+1(x+1)(x+2)+1(x+2)(x+3)+......+1(x+2013)(x+2014)=1x−1x+1+1x+1−1x+2+1x+2−1x+3+......+1x+2013−1x+2014=1x−1x+2014=2014xx+2014