Find the sum of series `4 - 9x + 16 x^(2) - 25 x^(3) + 36 x^(4) - 49 x^(5) + ...oo`

Explanation

To find the sum of the series \( S = 4 - 9x + 16x^2 - 25x^3 + 36x^4 - 49x^5 + \ldots \), we can follow these steps:

### Step 1: Identify the Series
The series can be expressed as:
\[ S = \sum_{n=1}^{\infty} (-1)^{n-1} n^2 x^{n-1} \]
where the coefficients are the squares of natural numbers multiplied by alternating signs.
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