Question

stabiliți daca n=36×1+37×3+..............36×999 este un patrat perfect

Answer 1

n=36×1+37×3+..............36×999 
n=1*36+3*36+.....+36*999
n=36(1+3+5+...+999) 

S.g = 1+3+5+.....+99
stabilim numarul de termeni:
999-1/2 +1 = 998/2+1 = 499+1 = 500

n=36*(1+999)*500/2
n=36*500*500
n=6²*500²
n=(6*500)²
n=3000²


R: n=3000² care este patrat perfect 


Numarul n=36×1+37×3+..............36×999 este patrat perfect!