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