Question

Tìm x

(x+1)+(2x+3)+(3x+5)+...+(50x+99)=3775

 

Answer 1

(x+1)+(2x+3)+(3x+5)+...+(50x+99)=3775

=> (x + 2x + 3x + ... + 50x) + (1 + 3 + 5 + ... + 99) = 3775

=> x . (1 + 2 +3 + ...+ 50) + (1 + 3 + 5 + ... + 99) = 3775

Áp dụng công thức tính dãy số ta có :

\(1+2+3+...+50=\frac{\left[\left(50-1\right):1+1\right].\left(50+1\right)}{2}=\frac{50.51}{2}=25.51=1275\)

\(1+3+5+...+99=\frac{\left[\left(99-1\right):2+1\right].\left(99+1\right)}{2}=\frac{50.100}{2}=50.50=2500\)

=> x . 1275 + 2500 = 3775

=> 1275x = 1275

=> x = 1