Telescoping Series

Calculus Level 1

( 1 2 − 1 3 ) + ( 1 3 − 1 4 ) + ( 1 4 − 1 5 ) + … + ( 1 2016 − 1 2017 ) \left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac {1}{3} -\frac{1}{4} \right) + \left(\frac{1}{4}- \frac{1}{5} \right) +\ldots+ \left(\frac {1}{2016} -\frac{1}{2017} \right)

What is the simplest fractional form of the sum above?

1007/2016 2014/4035 2015/4034 1/2017

Keshav Ramesh by Keshav Ramesh , 18, USA

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