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# Can someone help me please?

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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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Oct 12, 2019
#2
+440
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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