The sum of the series (1 + 0.6 + 0.06 + 0.006 | vedclass

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(A) The given series is $S = 1 + 0.6 + 0.06 + 0.006 + 0.0006 + \dots$We can write this as $S = 1 + (0.6 + 0.06 + 0.006 + 0.0006 + \dots)$.The part ins

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$1 \frac{2}{3}$

Vedclass · Answer

(A) The given series is $S = 1 + 0.6 + 0.06 + 0.006 + 0.0006 + \dots$We can write this as $S = 1 + (0.6 + 0.06 + 0.006 + 0.0006 + \dots)$.The part inside the bracket is an infinite Geometric Progression ($G.P.$) where the first term $a = 0.6$ and the common ratio $r = \frac{0.06}{0.6} = 0.1 = \frac{1}{10}$.The sum of an infinite $G.P.$ is given by the formula $S_{\infty} = \frac{a}{1 - r}$.Substituting the values, we get $S_{\infty} = \frac{0.6}{1 - 0.1} = \frac{0.6}{0.9} = \frac{6}{9} = \frac{2}{3}$.Therefore, the total sum $S = 1 + \frac{2}{3} = 1 \frac{2}{3}$.

The sum of the series $(1 + 0.6 + 0.06 + 0.006 + 0.0006 + \dots)$ is

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