Question

Suma tuturor nr nat care impartite la 7 dau catul 5

Answer 1

Răspuns:

266

Explicație pas cu pas:

$x : 7 = 5\:rest\:r, r < 7\\\\ x = 5\cdot 7 + r = 35 + r\\\\ S = 7\cdot 35 + 0 + 1 + 2 + 3 + 4 + 5 + 6\\\\\implies S = 245 + \frac{6\cdot 7}{2} = 245 + 3\cdot 7 = 245 + 21 = \\\\\boxed{S=266}$

Answer 2

Răspuns:

266

Explicație pas cu pas:

teorema impartirii cu rest

D=I*C=r

n=7*5+r...r∈{0;1;...6} pt ca r≤ I

n=7*5+0=35

n=7*5+1=36

n=7*5+2=37

..............

n=7*5+6=41

S=35+36+...+40+41= suma tip Gauss=(35+41)*7/2=76*7/2=38*7=266