Solution. Determine the common ratio, Since the common ratio r = 1 3 is a fraction between ā 1 and 1, this is a convergent geometric series. Use the first term a1 = 3 2 and the common ratio to calculate its sum. Sā = a1 1 ā r = 3 2 1 ā (1 3) = 3 3 2 3 = 3 2 ā
3 2 = 9 4. Answer: Sā = 9 4.
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But there is a faster way once you see the pattern. Make your chart for up to i^4. Then find the multiple of 4 closest, but less than the power. In this case 16 is the largest multiple of 4 less than 18. So i^16 = i^4 = 1. The count two more in the sequence. i^17 would be like i^1 = i. i^18 would be like i^2, or -1.
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3 4 1 5 answer