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Question

(C) Let $x = 0.5737373......$This can be written as $x = 0.5 + 0.0737373......$$x = 0.5 + \frac{73}{1000} + \frac{73}{100000} + \frac{73}{10000000} +

Vedclass · Accepted Answer

$\frac{568}{990}$

Vedclass · Answer

(C) Let $x = 0.5737373......$This can be written as $x = 0.5 + 0.0737373......$$x = 0.5 + \frac{73}{1000} + \frac{73}{100000} + \frac{73}{10000000} + ...$This is a geometric series starting from the second term with first term $a = \frac{73}{1000}$ and common ratio $r = \frac{1}{100}$.The sum of an infinite geometric series is $S = \frac{a}{1-r}$.$x = 0.5 + \frac{73/1000}{1 - 1/100} = \frac{5}{10} + \frac{73/1000}{99/100} = \frac{1}{2} + \frac{73}{1000} 	imes \frac{100}{99} = \frac{1}{2} + \frac{73}{990}$.$x = \frac{495 + 73}{990} = \frac{568}{990}$.

$0.5737373...... = $

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