Olympiad Question Problem

Question

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1144

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Hi. I need help with this question:

Find the integer part of:

\(\frac{1}{\frac{1}{2009}+\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}+\frac{1}{2015}}\)

Hint

1/1 + 1/2 = 3/2

1/2 + 1/3 = 5/6;

1/3 + 1/4 = 7/12;

1/4 + 1/5 = 9/20;

1/5 + 1/6 = 11/30 and so on.

MWizard2k04 Apr 1, 2017

edited by MWizard2k04 Apr 1, 2017

Ehrlich · Answer 1 · 2017-04-01T07:35:47

Lets call that expression 'x'.

Lets call the expression bellow the fault line 'y'.

7/2009>y>7/2015

So,

2009/7

287

So the integer part is 287.