Let  { 𝑎 𝑛 } 𝑛 = 0 ∞ ,   { 𝑏 𝑛 } 𝑛 = 0 ∞   and   { 𝑅 𝑛 } 𝑛 = 0 ∞  be POSITIVE sequences that are DIVERGENT TO ∞ . Assume that 𝑎 𝑛 << 𝑅 𝑛   and   𝑏 𝑛 << 𝑅 𝑛   . Which of the following statements must be true? Select all the correct answers.多项选择题

A

𝑎 𝑛 𝑏 𝑛 << 𝑅 𝑛 2

B

𝑎 𝑛 + 𝑏 𝑛 << 2 𝑅 𝑛

C

𝑎 𝑛 + 𝑏 𝑛 << 𝑅 𝑛

D

𝑎 𝑛 𝑏 𝑛 << 𝑅 𝑛

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Let  { 𝑎 𝑛 } 𝑛 = 0 ∞ , { 𝑏 𝑛 } 𝑛 = 0 ∞   and  { 𝑐 𝑛 } 𝑛 = 0 ∞   be positive sequences that are divergent to ∞ . Assume that 𝑎 𝑛 << 𝑏 𝑛 . Which of the following statements must be true? Select all the correct answers.

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