The sum of the series 1 + frac{4}{3} + frac{1 | vedclass

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(C) The given series is $S_n = 1 + \frac{4}{3} + \frac{10}{9} + \frac{28}{27} + \dots + n 	ext{ terms}$.We can rewrite the terms as:$S_n = (1) + (1 +

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$n + \frac{1}{2} - \frac{1}{2 \cdot 3^n}$

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(C) The given series is $S_n = 1 + \frac{4}{3} + \frac{10}{9} + \frac{28}{27} + \dots + n 	ext{ terms}$.We can rewrite the terms as:$S_n = (1) + (1 + \frac{1}{3}) + (1 + \frac{1}{9}) + (1 + \frac{1}{27}) + \dots + n 	ext{ terms}$.Grouping the terms,we get:$S_n = (1 + 1 + 1 + \dots + n 	ext{ times}) + (\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots + n 	ext{ terms})$.$S_n = n + \frac{\frac{1}{3}(1 - (\frac{1}{3})^n)}{1 - \frac{1}{3}}$.$S_n = n + \frac{\frac{1}{3}(1 - \frac{1}{3^n})}{\frac{2}{3}}$.$S_n = n + \frac{1}{2}(1 - \frac{1}{3^n})$.$S_n = n + \frac{1}{2} - \frac{1}{2 \cdot 3^n}$.

The sum of the series $1 + \frac{4}{3} + \frac{10}{9} + \frac{28}{27} + \dots$ up to $n$ terms is

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