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Question

(A) To simplify the expression,we evaluate each term in the product:
$\left(1-\frac{1}{2}\right) = \frac{1}{2}$
$\left(1-\frac{1}{3}\right) = \frac{

Vedclass · Accepted Answer

$\frac{1}{n}$

Vedclass · Answer

(A) To simplify the expression,we evaluate each term in the product:
$\left(1-\frac{1}{2}ight) = \frac{1}{2}$
$\left(1-\frac{1}{3}ight) = \frac{2}{3}$
$\left(1-\frac{1}{4}ight) = \frac{3}{4}$
Continuing this pattern,the last term is $\left(1-\frac{1}{n}ight) = \frac{n-1}{n}$.
Now,multiply all these terms together:
$\frac{1}{2} 	imes \frac{2}{3} 	imes \frac{3}{4} 	imes \cdots 	imes \frac{n-1}{n}$
Observe that the numerator of each fraction cancels out the denominator of the preceding fraction:
$\frac{1}{{2}} 	imes \frac{{2}}{{3}} 	imes \frac{{3}}{{4}} 	imes \cdots 	imes \frac{{n-1}}{n} = \frac{1}{n}$
Thus,the simplified value is $\frac{1}{n}$.

When simplified,the value of the product $\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right) \ldots\left(1-\frac{1}{n}\right)$ equals

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