Question

1/1*2 + 1/2*3 + 1/3*4 +...+ 1/2015*2016= ?????

Answer 1

$\frac{1}{1*2} =1- \frac{1}{2}$
$\frac{1}{2*3} = \frac{1}{2} - \frac{1}{3}$
$\frac{1}{3*4} = \frac{1}{3} - \frac{1}{4}$
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$\frac{1}{2014*2015} = \frac{1}{2014} - \frac{1}{2015}$
$\frac{1}{2015*2016} = \frac{1}{2015} - \frac{1}{2016}$
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$\frac{1}{1*2} + \frac{1}{2*3} + \frac{1}{3*4} +...+ \frac{1}{2015*2016} =1- \frac{1}{2016} = \frac{2016-1}{2016} = \frac{2015}{2016}$