Răspuns:
x = 2018.
Explicație pas cu pas:
1 / 1*2 + 1 / 2*3 + 1 / 3*4 + 1/ 4*5 + 1 / 5*6 + ... + 1 / x(x+1) =
1/1 - 1/2 +
1/2 - 1/3 +
1/3 - 1/4 +
1/4 - 1/5 +
1/5 - 1/6 +
- - - - - - - -
1/x - 1/(x+1) = unde se observa reducerile termenilor pe directii diagonale si ne ramane:
1 - 1(x+1).
1 - 1/(x+1) = 2018/2019
(x+1-1)/(x+1) = 2018/2019
x/(x+1) = 2018/2019
2019x = 2018(x+1)
2019x = 2018x + 2018
2019x - 2018x = 2018
x = 2018.
