Find the Radius of Convergence of the Series $$\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { ( x + 10 ) ^ { n } } { n 6 ^ { n } }$$

question 128

Multiple Choice

Find the radius of convergence of the series. Select the correct answer.
$$\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { ( x + 10 ) ^ { n } } { n 6 ^ { n } }$$

• A) \(( - 8,6 ]\)
• B) \(( 2,14 ]\)
• C) \(( - 14 , - 2 )\)
• D) \([ - 16 , - 4 )\)
• E) \([ - 1,1 ]\)

Differentiate between types of language rules and their application in constructing meaning.

Recognize the building blocks of language (phonemes, morphemes) and their functions.

Understand the cognitive strategies (heuristics and algorithms) used in problem-solving and decision-making.

Apprehend the significance of concepts, prototypes, and the structure of thought in cognitive processes.

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Definitions:

Linnaeus

Carl Linnaeus, an 18th-century Swedish botanist, physician, and zoologist who developed a system for naming, ranking, and classifying organisms.

Primates

Primates are an order of mammals that includes humans, apes, monkeys, and prosimians, characterized by complex behaviors, varied forms of locomotion, and a large brain relative to body size.

Hominids

Primates characterized by bipedalism and large brains, including the human lineage and all our immediate ancestors.

Genus

A rank in the biological classification system (taxonomy) that is used to group species sharing common characteristics, directly above species and below family.