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Rate of Convergence for Infinite Series

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Which of the following correctly ranks the infinite series below from the fastest rate of convergence to the slowest? A divergent series should be ranked as the slowest.

(i) ∑n=1∞13n\sum_{n=1}^{\infty} \frac{1}{3^n}
(ii) ∑n=1∞12n\sum_{n=1}^{\infty} \frac{1}{2^n}
(iii) ∑n=1∞1n2\sum_{n=1}^{\infty} \frac{1}{n^2}
(iv) ∑n=1∞1n\sum_{n=1}^{\infty} \frac{1}{n}

A

Series (i), Series (ii), Series (iii), Series (iv)

B

Series (ii), Series (i), Series (iii), Series (iv)

C

Series (iv), Series (iii), Series (ii), Series (i)

D

Series (i), Series (iii), Series (ii), Series (iv)

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