Question

Calculati suma tuturor numerelor naturale de doua cifre care se divid cu 11.

Answer 1

$S = 11+22+33+44+55+66+77+88+99\\ \\ S = 11\cdot (1+2+3+...+9)\\ \\ S = 11\cdot \dfrac{9\cdot (9+1)}{2} \\ \\ S = 11\cdot \dfrac{9\cdot 10}{2} \\ \\ S = 11\cdot 9\cdot 5 \\ \\ S = 11\cdot 45 \\ \\ \boxed{\boxed{S = 495}}$

Answer 2

a=11+22+33+44+55+66+77+88+99
2*a=(11+22+33+44+55+66+77+88+99)+(11+22+33+44+55+66+77+88+99)
2*a=110*9
2*a=990
a=495

Suma este egala cu 495