Question 184
Calculate the value of the sum $$
S = \frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + \cdots + \frac{1}{2006 \cdot 2007} + \frac{1}{2007 \cdot 2008}
$$
S = \frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + \cdots + \frac{1}{2006 \cdot 2007} + \frac{1}{2007 \cdot 2008}
$$