Răspuns:
Deducem o formula :
1/a*b = b-a/a*b = b/a*b - a/a*b =
= 1/a - 1/b
Unde b = a+1!!
S = 1/2*3 + 1/3*4 + ... + 1/2018*2019
S = 1/2 - 1/3 + 1/3 - 1/4 + ... +
1/2018 - 1/2019
1/3 se reduce
1/4 se reduce
...............
1/2018 se reduce
Ramane S = 1/2 - 1/2019
S = 2019/4038 - 2/4038
S = 2017/4038
