Question

Rezolvati ecuatia ;
1+2+3+... + 2002 totul supra 2002 - 2001 +2000 - 1999 + ... + 2 -1 toata fractia se aduna cu 7 = 1 + X + 2 + X + 3 + X + ... + 20 + X

Va rog cu rezolvare explicita .

Answer 1

1+2+3+... + 2002 = 2002 *2003/2=1001*2003


2002 - 2001 +2000 - 1999 + ... + 2 -1
2002-2001=1
2002:2=1001  deci vom avea 1001*1=1001

1 + X + 2 + X + 3 + X + ... + 20 + X
1+2+...20+20x=20*21/2+20x=210+20x

(1+2+3+...+2002)/(2002-2001+2000-1999+...+2-1)+7= 1+x+2+x+3+x+...+20 +x
1001*2003/1001+7=210+20x
2003+7=210+20x
2010-210=20x
1800=20x
x=90