Question

If $n \cdot 1 \cdot \frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot \frac{1}{5} = \frac{1}{2} \cdot \frac{1}{4} \cdot \frac{1}{6} \cdot \frac{1}{8} \cdot \frac{1}{10}$, what is the value of $n$? Express your answer as a common fraction.

Answer 1

3

Explanation:

trust me , it worked

Answer 2

`n\cdot1\cdot\frac12\cdot\frac13\cdot\frac14\cdot\frac15=\frac n{5!}`

`\frac12\cdot\frac14\cdot\frac16\cdot\frac18\cdot\frac1{10}=(3\cdot5\cdot7\cdot9)/(10!)`

So we have

`\frac n{5!}=(3\cdot5\cdot7\cdot9)/(10!)`

`n=(3\cdot5\cdot7\cdot9)/(6\cdot7\cdot8\cdot9\cdot10)`

`n=(3\cdot5)/(6\cdot8\cdot10)`

`n=\frac1{2\cdot8\cdot2}`

`n=\frac1{32}`