n = 49 x 1 + 49 x 3 + 49 x 5 + ......+ 49 x 999
n = 49 x ( 1 + 3 + 5 + ........+ 999 )
1 + 3 + 5 + ........+ 999 = 500 x ( 1 + 999 ) / 2 = 500 x 1 000 / 2 = 500 x 500
→ stabilim cati termeni are suma, ratia fiind 2 ( 3 - 1 = 2; 5 - 3 = 2 )
→ apli formula sumei lui Gauss
( 999 - 1 ) : 2 + 1 = 998 : 2 + 1 = 499 + 1 = 500 termeni are suma
n = 49 x 500 x 500
n = 7² x 500²
n = ( 7 x 500 )² → patrat perfect
