Question

Rezolvați ecuația:
x+2x+3x......+100x=50500
Va rog frumos!!!!

Answer 1

x(1+2+3+....100)=50500
suma 1+2+3+...100=100*101/2=5050 => x*5050=50500 => x=50500/5050=10

Answer 2

$\displaystyle x+2x+...+100x=50500 \\ \\ x(1+2+...+100)=50500 \\ \\ x \cdot \frac{100(100+1)}{2} =50500 \\ \\ x \cdot \frac{100 \times 101}{2} =50500 \\ \\ x \cdot \frac{10100}{2} =50500 \\ \\ x \cdot 5050=50500 \\ \\ 5050x=50500 \\ \\ x= \frac{50500}{5050} \\ \\ x=10$