Question

X+2X+3X+...+100X = -1+2-3+4-...-201+202

Answer 1

x+2x+3x+...+100x = -1+2-3+4-...-201+202 
x(1+2+3+...100)=1+1+....+1 
x *100*101/2=1*202/2 
5050x=101  
x=101/5050
x=1/50

Answer 2

x+2x+3x+.....+100x=-1+2-3+4-....-201+202
Dam factor comun pe x:
x*(1+2+3+...+100)=(-1+2)+(-3+4)+.....+(-201+202)
x*[100*(100+1):2]=1+1+1+.....+1(101 de 1)
x*(100*100:2)=1*101
x*(10100:2)=101
x*5050=101
x=101:5050(simplificam cu 101)
x=1:50∈Q