Question

The product of the $9$ fractions $\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)..........\left(1-\frac{1}{10}\right)=$____________.

• A. $\frac{10}{11}$
• B. $\frac{1}{9}$
• C. $\frac{1}{10}$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$\frac{1}{10}$

We need to simplify $(1-\frac{1}{2})(1-\frac{1}{3})(1-\frac{1}{4}).....(1-\frac{1}{10})$

Simplifying each bracket, we get

$\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}.......\frac{7}{8}\times \frac{8}{9}\times \frac{9}{10}$

As we can see

Starting from $1^{st}$ term, each denominator is cancelled out by next numerator.

Finally we get $\frac{1}{10}$