Question

REZOLVATI ECUATIA :
X+2X+3X+.........+100X=50.500

Answer 1

X+2X+3X+.........+100X=50500
x*(1+2+3+...+100)=50500
folosim formula lui Gauss
x*(100*101:2)=50500
x*5050=50500
x=50500:5050
x=10

Answer 2

$\displaystyle x+2x+3x+...+100x=50500 \\ \\ x(1+2+3+...+100)=50500 \\ \\ x \cdot \frac{100(100+1)}{2} =50500 \\ \\ x \cdot \frac{100 \times 101}{2} =50500 \\ \\ x \cdot \frac{10100}{2} =50500 \\ \\ x \cdot 5050=50500 \\ \\ 5050x=50500 \\ \\ x= \frac{50500}{5050} \\ \\ \boxed{x=10}$