Let 𝑆 = ∑ 𝑛 = 0 ∞ 𝑎 𝑛 be a series. Which of the following statements must be true? Select all the correct answers.Multiple choice

A

IF lim 𝑛 → ∞ 𝑎 𝑛 ≠ 0 , THEN the series S is DIVERGENT.

B

IF the series S is DIVERGENT, THEN lim 𝑛 → ∞ 𝑎 𝑛 = 0 .

C

IF lim 𝑛 → ∞ 𝑎 𝑛 = 0 , THEN the series S is CONVERGENT.

D

IF ∑ 𝑛 = 1 ∞ 𝑎 𝑛 is DIVERGENT, THEN ∑ 𝑛 = 1 ∞ 𝑎 𝑛 = ∞

E

IF ∑ 𝑛 = 1 ∞ 𝑎 𝑛 is DIVERGENT, THEN lim 𝑛 → ∞ 𝑎 𝑛 ≠ 0 .

F

IF the series S is CONVERGENT, THEN lim 𝑛 → ∞ 𝑎 𝑛 = 0 .

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