Question

tính tổng A=1/1.2+1/2.3+..........+1/2003.2004

Answer 1

=1-1/2+1/2-1/3+...+1/2003-1/2004

=1-1/2004

=2003/2004

Answer 2

Lời giải:

$A=\frac{2-1}{1.2}+\frac{3-2}{2.3}+...+\frac{2004-2003}{2003.2004}$

$=\frac{2}{1.2}-\frac{1}{1.2}+\frac{3}{2.3}-\frac{2}{2.3}+....+\frac{2004}{2003.2004}-\frac{2003}{2003.2004}$

$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-....+\frac{1}{2003}-\frac{1}{2004}$

$=1-\frac{1}{2004}=\frac{2003}{2004}$