Determine Whether Each of the Following Series Is Convergent or Divergent.(a)

question 206

Short Answer

Determine whether each of the following series is convergent or divergent.(a) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { 2 + 3 ^ { - n } }$ (b) $\sum _ { n = 0 } ^ { \infty } \frac { \pi ^ { n } } { 3 ^ { n } }$ (c) $\sum _ { n = 1 } ^ { \infty } \frac { e ^ { n } } { 3 ^ { n } }$

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Definitions:

Sea Lamprey

An invasive, parasitic fish known for its detrital impact on native fish species in the Great Lakes and other fresh water environments.

Welland Canal

A ship canal in Canada, connecting Lake Ontario and Lake Erie, facilitating navigation and trade by bypassing Niagara Falls.

Ballast Water

Water carried in ships' ballast tanks to improve stability and balance, which, when discharged, can introduce invasive aquatic species to new environments.

Autonomy

The degree to which a job provides the employee with the freedom, independence, and discretion to schedule their work and determine how it is done.