numitorul
-1/2-2/3-3/4-....-2016/2017=-(1/2+2/3+3/4+.....+2016/2017)
1/2=2/2-1/2; 2/3=3/3-1/3.........2016/2017=2017/2017-1/2017
numitorul devine:
2016 -(2/2 -1/2 +3/3-1/3+......+2017/2017-1/2017)
= 2016 -2016 -(1/2-1/3+.......-1/2017)= + (1/2 + 1/3 + 1/4 +...+ 1/2017)
x = (1/2 + 1/3 + 1/4 +...+ 1/2017) / (2016 - 1/2 - 2/3 - 3/4 - ... - 2016/2017)
devine
x = (1/2 + 1/3 + 1/4 +...+ 1/2017)/(1/2 + 1/3 + 1/4 +...+ 1/2017)
x = 1
