If left(1-frac{1}{2}right)left(1-frac{1}{3}ri | vedclass

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(D) Given the expression: $\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right) \cdots\left(1-\frac{1}{70}\right)=\frac{x}{7

Vedclass · Accepted Answer

$1$

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(D) Given the expression: $\left(1-\frac{1}{2}ight)\left(1-\frac{1}{3}ight)\left(1-\frac{1}{4}ight) \cdots\left(1-\frac{1}{70}ight)=\frac{x}{70}$
Simplify each term in the product:
$\left(\frac{2-1}{2}ight)\left(\frac{3-1}{3}ight)\left(\frac{4-1}{4}ight) \cdots\left(\frac{70-1}{70}ight)=\frac{x}{70}$
This results in:
$\frac{1}{2} 	imes \frac{2}{3} 	imes \frac{3}{4} 	imes \cdots 	imes \frac{69}{70}=\frac{x}{70}$
Observe the telescoping pattern where the numerator of each fraction cancels with the denominator of the preceding fraction:
$\frac{1}{{2}} 	imes \frac{{2}}{{3}} 	imes \frac{{3}}{{4}} 	imes \cdots 	imes \frac{{69}}{70} = \frac{1}{70}$
Equating this to the given expression:
$\frac{1}{70} = \frac{x}{70}$
Therefore,$x = 1$.

If $\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right) \ldots\left(1-\frac{1}{70}\right)=\frac{x}{70},$ then what is the value of $x ?$

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