left(1-frac{1}{3}right)left(1-frac{1}{4}right | vedclass

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Question

(A) The given expression is $\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right) \ldots \left(1-\frac{1}{25}\right)$.
Simp

Vedclass · Accepted Answer

$\frac{2}{25}$

Vedclass · Answer

(A) The given expression is $\left(1-\frac{1}{3}ight)\left(1-\frac{1}{4}ight)\left(1-\frac{1}{5}ight) \ldots \left(1-\frac{1}{25}ight)$.
Simplifying each term:
$= \left(\frac{3-1}{3}ight) 	imes \left(\frac{4-1}{4}ight) 	imes \left(\frac{5-1}{5}ight) 	imes \ldots 	imes \left(\frac{25-1}{25}ight)$
$= \frac{2}{3} 	imes \frac{3}{4} 	imes \frac{4}{5} 	imes \ldots 	imes \frac{23}{24} 	imes \frac{24}{25}$
Observing the pattern,the numerator of each fraction cancels out the denominator of the preceding fraction.
$= \frac{2}{{3}} 	imes \frac{{3}}{{4}} 	imes \frac{{4}}{{5}} 	imes \ldots 	imes \frac{{24}}{25}$
$= \frac{2}{25}$

$\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right) \ldots \left(1-\frac{1}{25}\right)$ is equal to

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