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If the sum to infinity of the series 3+(...

If the sum to infinity of the series `3+(3+d)1/4+(3+2d)1/(4^2)+oo` is `(44)/9` , then find `ddot`

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To find the value of \( d \) in the series given by \( 3 + (3 + d) \frac{1}{4} + (3 + 2d) \frac{1}{4^2} + \ldots \) with a sum to infinity of \( \frac{44}{9} \), we can follow these steps: ### Step 1: Write the series in summation form The series can be expressed as: \[ S = 3 + (3 + d) \frac{1}{4} + (3 + 2d) \frac{1}{4^2} + \ldots \] ...
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