Найти сумму 1/1*2 * 1/2*3 + 1/3*4 +...+ 1/2006*2007

[latex] \frac{1}{1*2} + \frac{1}{2*3} + \frac{1}{3*4} + ...+ \frac{1}{2006*2007}= \\ = \frac{2-1}{1*2} + \frac{3-2}{2*3} + \frac{4-3}{3*4} + ...+ \frac{2007-2006}{2006*2007}= \\ = \frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3}+ \frac{1}{3} - \frac{1}{4} + ...+ \frac{1}{2006} - \frac{1}{2007} = \\ = 1 - \frac{1}{2007} = \frac{2006}{2007} [/latex]