Răspuns: x = 1003
Explicație pas cu pas:
(1+2+3+....+2004)/(2+4+6+....+2004) = (2x-1)/x
Calculez sumele:
2004×(1+2004):2 = 1002 ×2005 -> numaratorul
2×(1+2+3+...+1002)= 2×1002 ×(1+1002):2 = 1002 × 1003 -> numitorul
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(1002× 2005)/(1002×1003) = (2x-1)/x
-> simplific prima fractie prin 1002
2005/1003 = (2 x -1)/x
2005 x = 1003×(2x - 1) → produsul mezilor = produsul extremilor
2005 x = 2006 x - 1003
2006 x - 1003 = 2005 x
2006 x - 2005 x = 1003
x = 1003
[tex]\frac{1+2+..+2004}{2+4+..+2004}=\frac{2x-1}{x}\\\\\frac{2004*2005:2}{2(1002*1003:2)}=\frac{2x-1}{x}\\\\\frac{1002*2005}{1002*1003}=\frac{2x-1}{x}[/tex]
2005x=1003(2x-1)
2005x=2006x-1003
1003=2006x-2005x
x=1003
