Question

x+2x+3x+...+100x=50500
x=?

Answer 1

$x + 2x + 3x + ... + 100x = 50500 \\ x(1 + 2 + 3 + ... + 100) = 50500 \\ x \times \frac{100 \times 101}{2} = 50500 \\ x \times 50 \times 101 = 50500 \\ x \times 5050 = 50500 \\ x = 10$

Answer 2

Răspuns:

10

Explicație pas cu pas:

$x+2x+3x+...+100x=50500 \\ x \cdot (1 + 2 + 3 + ... + 100) = 50500$

$x \cdot \dfrac{100 \cdot (100 + 1)}{2} = 50500 \\ x \cdot \dfrac{100 \cdot 101}{2} = 50500 \\ x \cdot 5050 = 50500 \implies x = \dfrac{50500}{5050} \\ \implies \bf x = 10$