Question

Efectuati: 4+5-6+7+8-9+10+11-12+.........+106+107-108

Answer 1

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

Answer 2

$\displaystyle \sum\limits_{k=1}^{35}\big[(3k+1)+(3k+2)-(3k+3)\big] =$

$\displaystyle =\sum\limits_{k=1}^{35}(3k+3k-3k+1+2-3)=$

$\displaystyle =\sum\limits_{k=1}^{35}(3k) = 3\sum\limits_{k=1}^{35}k = 3\cdot \dfrac{35\cdot (35+1)}{2} =$

$=3\cdot \dfrac{35\cdot 36}{2} =3\cdot 35\cdot 18 = \boxed{1890}$