Which of the Following Three Tests Will Establish That the Series

question 305

Multiple Choice

Which of the following three tests will establish that the series $\sum _ { n = 1 } ^ { \infty } \frac { n } { \sqrt { 7 n ^ { 3 } + 46 } }$ diverges?
1) Limit Comparison Test with $\sum _ { n = 1 } ^ { \infty } n ^ { - 1 }$
2) Comparison Test with $\sum _ { n = 1 } ^ { \infty } n ^ { - 1 }$
3) Comparison Test with $\sum _ { n = 1 } ^ { \infty } n ^ { - 1 / 2 }$

• A)None
• B)1
• C)2
• D)3
• E)1, 2
• F)1, 3
• G)2, 3
• H)1, 2, 3

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Definitions:

Essential Amino Acid

An amino acid that must be provided in the diet because the body cannot make it or cannot make it in sufficient quantities to meet nutritional needs.

Synthesize

The process of combining different elements or components to form a coherent whole, especially in the context of producing chemical compounds or complex ideas.

Sufficient Amounts

Quantities or volumes that are adequate for meeting needs, requirements, or purposes specified in a particular context.

Steroids

A large class of organic compounds with a characteristic molecular structure containing four rings; they include many hormones, alkaloids, and vitamins.