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Sum to infinite terms of a gp - class-XI
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The value of $3 - 1 + \frac{1}{3} - \frac{1}{9} + \ldots $ is equal to
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A
$\dfrac{{9}}{4}$
💡 Explanation:
The series is 3 - 1 + 1/3 - 1/9 + ... which can be split into 3 + (-1 + 1/3 - 1/9 + ...). The part in parentheses is a geometric series with first term a = -1 and common ratio r = -1/3. The sum is a / (1 - r) = -1 / (1 - (-1/3)) = -1 / (4/3) = -3/4. Adding the initial 3 gives 3 - 3/4 = 9/4.