Find the sum to ininity of the series `1-3x+5x^2+7x^3+..... oo` when Ix| <1.

Explanation

To find the sum to infinity of the series \( S = 1 - 3x + 5x^2 - 7x^3 + \ldots \) when \( |x| < 1 \), we can follow these steps:

### Step 1: Identify the series
The series can be rewritten as:
\[ S = 1 + (-3)x + 5x^2 + (-7)x^3 + \ldots \]
This series has alternating signs and can be expressed in a more manageable form.
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