If A = left(frac{1}{0.4}right) + left(frac{1} | vedclass

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(C) The given series is $A = \frac{1}{0.4} + \frac{1}{0.04} + \frac{1}{0.004} + \dots$ up to $8$ terms.We can rewrite the terms as:$A = 2.5 + 25 + 250

Vedclass · Accepted Answer

$27777777$

Vedclass · Answer

(C) The given series is $A = \frac{1}{0.4} + \frac{1}{0.04} + \frac{1}{0.004} + \dots$ up to $8$ terms.We can rewrite the terms as:$A = 2.5 + 25 + 250 + 2500 + \dots$ up to $8$ terms.This is a Geometric Progression $(GP)$ where the first term $a = 2.5$ and the common ratio $r = 10$.The sum of the first $n$ terms of a $GP$ is given by $S_n = \frac{a(r^n - 1)}{r - 1}$.Here,$n = 8$,$a = 2.5$,and $r = 10$.$A = \frac{2.5(10^8 - 1)}{10 - 1} = \frac{2.5(100000000 - 1)}{9} = \frac{2.5 	imes 99999999}{9}$.$A = 2.5 	imes 11111111 = 27777777.5$.

If $A = \left(\frac{1}{0.4}\right) + \left(\frac{1}{0.04}\right) + \left(\frac{1}{0.004}\right) + \dots$ up to $8$ terms,then what is the value of $A$ (in $.5$)?

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