Question

Va rog frumos !! Dau cel mai inteligent raspuns !! Nu vreau sa consum punctele punand aceeasi intrebare mereu!!
Aratati ca n=49.1+49.3+49.5+....49.999 este un patrat perfect

Answer 1

n= 49·1+ 49·3+ 49·5+ ... + 49· 999   pp= ?
n= 49( 1+ 3+ 5+ 999)
n= 49·[1+ (1+2)- (1+ 4)+ ...+( 1+ 998)]
n= 49·[ (1+1+ ...+ 1)+ ( 2+ 4+ ...+ 998)]
n= 49·[ 1·500+ 2·(1+ 2+ ...+ 499)]
n= 49·[500+ 2·499·500:2]
n= 49·(500+499·500)
n= 49·[500·( 1+ 499)]
n= 49· 500·500
n= 7²·500²
n= (7·500)²
n= (3 500)²  ⇒         (3 500)²    =pp