In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 6 Σ (i = 1) (1/2)^(i + 1)

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1. Identify the sequence as a geometric sequence with the general term \( a_i = \left(\frac{1}{2}\right)^{i+1} \).
2. Determine the first term \( a_1 \) by substituting \( i = 1 \) into the general term: \( a_1 = \left(\frac{1}{2}\right)^{1+1} = \left(\frac{1}{2}\right)^2 \).
3. Identify the common ratio \( r \) of the geometric sequence, which is \( \frac{1}{2} \).
4. Use the formula for the sum of the first \( n \) terms of a geometric sequence: \( S_n = a_1 \frac{1-r^n}{1-r} \), where \( n = 6 \).
5. Substitute \( a_1 = \left(\frac{1}{2}\right)^2 \), \( r = \frac{1}{2} \), and \( n = 6 \) into the sum formula to find \( S_6 \).