Question

Solutia ecuatiei 1 + 5 + 9 +....+ X=2016


Dau coroana!​

Answer 1

1+5+9+...+x = 2016

1+(2+3)+(4+5)+...+((x-1)/2+(x+1)/2) = 2016

1+2+3+4+5+...+(x+1)/2 = 2016

Aplicam formula lui Gauss:

(x+1)/2•[(x+1)/2+1]/2 = 2016

(x+1)/2•[(x+3)/2]/2 = 2016

(x+1)(x+3)/8 = 2016

(x+1)(x+3) = 2016•8

(x+1)(x+3) = 1008•16

(x+1)(x+3) = 126•8•16

(x+1)(x+3) = 126•128

=> x = 125