Question

Find the value of $(1-\frac{1}{3^2})(1-\frac{1}{4^2})(1-\frac{1}{5^2}).....(1-\frac{1}{{11}^2})(1-\frac{1}{{12}^2})$

• A. $\frac{17}{18}$
• B. $\frac{13}{18}$
• C. $\frac{1}{144}$
• D. $\frac{1}{9}$

Answer 1

The correct option is B $\frac{13}{18}$

$(1-\frac{1}{3^2})(1-\frac{1}{4^2})(1-\frac{1}{5^2}).....(1-\frac{1}{{11}^2})(1-\frac{1}{{12}^2})$
$\Rightarrow (1-\frac{1}{9})(1-\frac{1}{16})(1-\frac{1}{25}).....(1-\frac{1}{121})(1-\frac{1}{144})$
$\Rightarrow \frac{8}{9}\times \frac{15}{16}\times \frac{24}{25}........\frac{120}{121}\times \frac{143}{144}$
$\Rightarrow \frac{13}{18}$