Question

Stabiliti daca n= 49 • 1+49•3+....+49•999 este un patrat perfect

Answer 1

Ai rezolvarea in poza.

Answer 2

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