Question

Rezolvați ecuația :

x-1/2 + 2x-1/3 + 3x-1/4 + ... + 2007x-1/2008 = 1/2 + 2/3 + ... + 2007/2009 -2007

Answer 1

x-1/2 + 2x-1/3 + 3x-1/4 + ... + 2007x-1/2008 = 1/2 + 2/3 + ... + 2007/2008 -2007

x+2x+3x+….+2007x=1/2+1/2+2/3+1/3+…+2007/2008+1/2008 -2007

x(2007•2008/2)=2/2+3/3+…+2008/2008 -2007

de la 2 la 2008 sunt 2007 numere

=> x•1004•2007=2007-2007

x•1004•2007=0

=> x=0