Question

The value of $(1-\frac{1}{3})(1-\frac{1}{4})(1-\frac{1}{5})...(1-\frac{1}{n})$ is equal to

• A. $\frac{1}{n}$
• B. $\frac{2}{n}$
• C. $\frac{3}{n}$
• D. $\frac{4}{n}$

Answer 1

The correct option is B $\frac{2}{n}$

$(1-\frac{1}{3})(1-\frac{1}{4})(1-\frac{1}{5}).........(1-\frac{1}{n})=\frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}\times ....................\frac{n-2}{n-1}\times \frac{n-1}{n}$

So all the numerators and denominators of expression are cancelled except $2$ in the numerator of the first factor and $n$ in the denominator of the last factor. So, the result is $\frac{2}{n}$