Question

Nếu 2+4+6+8+...+2x(X+1)=61752 tìm X    

Answer 1

2+4+6+8+…+2.(x+1)=61752

=>2.[1+2+3+4+…+(x+1)]=61752

=>\(2.\frac{\left(x+1\right).\left(x+1+1\right)}{2}=61752\)

=>(x+1).(x+2)=61752=248.249

=>(x+1).(x+2)=(247+1).(247+2)

=>x=247

Vậy x=247

Answer 2

Đặt S=2+4+6+....+2.(x+1)

Số số hạng là:(2.(x+1)-2):2+1=2.(x+1-1):2+1=x+1

số cặp là:\(\frac{x+1}{2}\)

giá trị 1 cặp là:2.(x+1)+2

S=\(\frac{x+1}{2}\).2.(x+1)+2=x+1.(x+1)+2

Ta có:x+1.(x+1)+2=61752=...............