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Question
Find the sum of the following serie to infinity:
\[1 - \frac{1}{3} + \frac{1}{3^2} - \frac{1}{3^3} + \frac{1}{3^4} + . . . \infty\]
Solution
\[\text { In the given G . P . , first term, } a = 1 \]
\[\text { and common ratio } , r = - \frac{1}{3}\]
\[\text { Hence, the sum S to infinity is given by } S = \frac{a}{1 - r} = \frac{1}{1 - \left( - \frac{1}{3} \right)} = \frac{3}{4} . \]
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