Step 1:
First, we rewrite the given series as follows:
$$\sum_{n=1}^{\infty}(-1)^{n+1} \frac{1}{2^{n} n} = \sum_{n=1}^{\infty}(-1)^{n+1} \frac{1}{n} \left(\frac{1}{2}\right)^n$$
Here, we have simply moved the 1/2 in the numerator to the base of the exponent.
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