In an infinite geometric series with first term 8 and common ratio 1/2, what is its sum?

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Multiple Choice

In an infinite geometric series with first term 8 and common ratio 1/2, what is its sum?

Explanation:
An infinite geometric series converges to a sum S = a/(1 − r) when the absolute value of the common ratio is less than 1. Here the first term is 8 and the common ratio is 1/2, which satisfies |r| < 1. So the sum is 8 / (1 − 1/2) = 8 / (1/2) = 16. You can also see this by the partial sums: 8, 12, 14, 15, 15.5, …, which approach 16.

An infinite geometric series converges to a sum S = a/(1 − r) when the absolute value of the common ratio is less than 1. Here the first term is 8 and the common ratio is 1/2, which satisfies |r| < 1. So the sum is 8 / (1 − 1/2) = 8 / (1/2) = 16. You can also see this by the partial sums: 8, 12, 14, 15, 15.5, …, which approach 16.

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