Determine whether the series is convergent or divergent. (1/3) + (1/6) + (1/9) + (1/12) + (1/15) ...

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Mathematics

Yael Carey

11 March, 18:01

Determine whether the series is convergent or divergent. (1/3) + (1/6) + (1/9) + (1/12) + (1/15) ...

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Hallie Boyle · Answer 1

The given series (1/3) + (1/6) + (1/9) + (1/12) + (1/15) ... is an infinite geometric series. The geometric ratio from the series is 1/3. Hence the series is convergent because the ratio is less than 1. Convergent means the sum of the numbers of this series is a definite number because the numbers in the later orders become negligible then.