Sa se determine partea intreaga a nr N= [latex] \frac{1}{1*2} [/latex]+[latex] \frac{1}{2*3} [/latex]......+[latex] \frac{1}{2007*2008} [/latex]

N= 1/(1*2) + 1/(2*3) +.....+1/(2007*2008) 1/(1*2)= 1/1 -1/2 1/(2*3)= 1/2 -1/3 1/(3*4)= 1/3 -1/4 ............................................ 1/(2006*2007)= 1/2006 -1/2007 1/(2007*2008)= 1/2007- 1/2008 N= 1/1 -1/2008  aducem la acelasi numitor N=(2008-1)/2008=  2007/2008=  0,999  (partea intreaga este 0)