The sum of the series `1/(2!)-1/(3!)+1/(4!)-...` upto infinity is (1) `e^(-2)` (2) `e^(-1)` (3) `e^(-1//2)` (4) `e^(1//2)`

Explanation

To find the sum of the series \( S = \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \frac{1}{5!} + \ldots \) up to infinity, we can relate it to the exponential function.

### Step-by-Step Solution:

1. **Recognize the Series**: The series can be rewritten as:
\[ S = \sum_{n=2}^{\infty} \frac{(-1)^{n}}{n!} \]
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