Question

Calculează sumele 1+3+5+.....+177=

Answer 1

1+3+5+...+117=
1+2+3+4+5+6+...+176+176-(2+4+6+...+176)
aplicam formula lui Gaus care era:
1+2+3+...n=n (n+1)supra 2


$\frac{177(177 + 1)}{2} - \frac{176(176 + 1)}{2} =$
$\frac{177 \times178 }{2} - \frac{176 \times 177}{2} =$
$177 \times 89 -88 \times 177 =$
dam factor comun pe 177

$177(89 - 88) \\ 177 \times 1 = 177$