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Let \(\frac{m}{n}\) be a fraction, where \(m\) and \(n\) are positive integers. Consider the operation defined by replacing \(\frac{m}{n}\) by \(\frac{m+1}{n+1}\) and then writing the result in lowest terms. For example, applying this operation to \(\frac{5}{14}\) would give \(\frac{2}{5}\). How many times must this operation be repeatedly applied to \(\frac{1}{2005}\) before we obtain \(\frac{2004}{2005} \).

 Oct 12, 2019
 #1
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See the answer here:  https://web2.0calc.com/questions/can-u-please-help_1

 Oct 12, 2019
 #2
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+5

1 / 1005
1 / 1003
1 / 502
2 / 503
1 / 168
2 / 169
3 / 170
This continues until you get: 166 / 333 + 1
165 / 332
166 / 333
1 / 2
2 / 3
3 / 4 - This continues until you get: 2004 / 2005
2001 / 2002
2002 / 2003
2003 / 2004
2004 / 2005
TOTAL TERMS = 2,174

 Oct 13, 2019

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