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If the sum to infinity of the series 1 +...

If the sum to infinity of the series `1 + 4x + 7x^2 + 10x^3 +.............` is `35/16` then `x=` (A) `1/5` (B) `2/5` (C) `3/7` (D)`1/7`

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AI Generated Solution

To solve the problem, we need to find the value of \( x \) for which the sum to infinity of the series \( 1 + 4x + 7x^2 + 10x^3 + \ldots \) equals \( \frac{35}{16} \). ### Step-by-Step Solution: 1. **Identify the Series**: The series can be expressed as: \[ S = 1 + 4x + 7x^2 + 10x^3 + \ldots ...
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