Question

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

Answer 1

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)