If a Series of Constants $\sum a_{k}$ Diverges, Then Must $\sum\left|\alpha_{k}\right|$ Diverge

question 17

Short Answer

If a series of constants $\sum a_{k}$ diverges, then must $\sum\left|\alpha_{k}\right|$ diverge?

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Definitions:

Toxic Substances Control Act

U.S. legislation enacted to regulate the introduction of new or already existing chemicals, with the aim of protecting human health and the environment.

Unreasonable Risk

A situation or action that exposes individuals to a significant potential for harm that is not justified by the possible benefits.

Human Health

The state of complete physical, mental, and social well-being, not merely the absence of disease or infirmity.

Toxic Substances Control Act

A legislation passed in the United States in 1976 designed to control the introduction and use of both new and existing chemicals.