Question

Calculati prin formula lui Gauss :
a) 8+16+24+...+2504 =?
b) 11+22+33+...+1331=?
c)19 +38+57+...+1995=?
Dau coroană !!!!!!

Answer 1

$\displaystyle \boxed{ \frac{n(n+1)}{2}} \\ \\ \text{n= ultimul numar din sir ; se aplica la sirul 1+2+3+...+n} \\ \\ a)8+16+24+...+2504 = \\ \\ \text{factor comun pe 8} \\ \\ 8(1+2+3+...+313) \\ \\ (1+2+3+...+313)= \frac{313\cdot314}{2}=49141 \\ \\ 8\cdot49141=\underline{393.128 } \\ \\ ============ \\ \\ b)11+22+33+...+1331= \\ \\ \text{factor comun pe 11} \\ \\ 11(1+2+3+...121)= \\ \\ (1+2+3+...121)= \frac{121\cdot122}{2} = 7381 \\ \\11\cdot7381=\underline{81.191} \\ \\===========$