Question

Cum rezolv x+(2x-1)+(3x-2)+(4x-3)+...+(51x-50)=51

Answer 1

   
[tex]\displaystyle\\ x+(2x-1)+(3x-2)+(4x-3)+\cdots+(51x-50)=51\\\\ (x+2x+3x+4x+\cdots +51x)-(1+2+3+4+\cdots +50) =51\\\\ x(1+2+3+4+\cdots +51) -(1+2+3+4+\cdots +50)=51\\\\ x(1+2+3+4+\cdots +51) = 51 +(1+2+3+4+\cdots +50)\\\\ x(1+2+3+4+\cdots +51) = 1+2+3+4+\cdots +50+51\\\\ x(1+2+3+4+\cdots +51) = 1+2+3+4+\cdots +51\\\\ x = \frac{ 1+2+3+4+\cdots +51}{1+2+3+4+\cdots +51} = \boxed{1}[/tex]