Question
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum.$$\sum_{k=1}^{\infty} \frac{1}{2} \cdot 3^{k-1}$$
Step 1
The given series is \[ \sum_{k=1}^{\infty} \frac{1}{2} \cdot 3^{k-1}. \] The first term \( a \) is obtained by substituting \( k = 1 \): \[ a = \frac{1}{2} \cdot 3^{1-1} = \frac{1}{2} \cdot 3^0 = \frac{1}{2}. \] The common ratio \( r \) is the factor by which Show more…
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