Răspuns:
Explicație pas cu pas:
4+5-6+7+8-9+10+11-12+.........+106+107-108 are 105 termeni
4+5-6 = 3
7+8-9 = 6
10+11-12 = 9
.......
106+107-108 = 105
Relatia initiala devine
3 + 6 + 9 + ...+ 105 si are 105 : 3 = 35 termeni
S = 35*(3 + 105)/2 = 35*108/2 = 1890
[tex]\displaystyle \sum\limits_{k=1}^{35}\big[(3k+1)+(3k+2)-(3k+3)\big] =[/tex]
[tex]\displaystyle =\sum\limits_{k=1}^{35}(3k+3k-3k+1+2-3)=[/tex]
[tex]\displaystyle =\sum\limits_{k=1}^{35}(3k) = 3\sum\limits_{k=1}^{35}k = 3\cdot \dfrac{35\cdot (35+1)}{2} =[/tex]
[tex]=3\cdot \dfrac{35\cdot 36}{2} =3\cdot 35\cdot 18 = \boxed{1890}[/tex]
