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# Algebra

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If $\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot...\cdot\frac{n}{n+1} = \frac{1}{10}$, what is the sum of the numerator and denominator of the largest fraction on the left side of the equation?

Apr 29, 2022

#1
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$$\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot...\cdot\frac{n}{n+1} = \frac{1}{10}$$

We can write this in a slightlly different manner

2 *  3/3 * 4/4 * 5/5  *  ......* 19/19  *  1 / 20

The largest  fraction will be  19  /  20

So.....the sum =   39

Apr 29, 2022