Question

Rezolva ecuatia:
X+2x+3x+..............+100x=50500

Answer 1

$x+2x+3x+.....+100x=50500$
Dam factor comun pe x:
$x*(1+2+3+...+100)=50500$
Calculam paranteza cu ajutorul sumei Gauss pentru numere consecutive:
$x*(\frac{100*(100+1)}{2})=50500 \\ x*(\frac{100*101}{2})=50500 \\ x*(\frac{10100}{2})=50500 \\ x*5050=50500 \\ x=\frac{50500}{5050} \\ x=10$

Answer 2

x+2x+3x+......+100x=50500
x(1+2+3+....+100)=50500
x{[(1+100) ori 100]:2}=50500
x{(101 ori100):2]=50500
x(10100:2)=50500
x ori 5050=50500
x=50500:5050
x=10