Find the sum of the series `1-3x+5x^2-7x^3+ ton` terms.

Explanation

To find the sum of the series \( S_n = 1 - 3x + 5x^2 - 7x^3 + \ldots \) up to \( n \) terms, we can follow these steps:

### Step 1: Identify the Pattern
The series can be expressed as:
\[ S_n = \sum_{k=0}^{n-1} (-1)^k (2k + 1) x^k \]
This shows that the coefficients of \( x^k \) are \( (-1)^k (2k + 1) \).
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