Determine Whether the Series $\sum _ { n = 0 } ^ { \infty } \frac { 1 + \sin ^ { 2 } n } { 5 ^ { n } }$

question 111

Short Answer

Determine whether the series $\sum _ { n = 0 } ^ { \infty } \frac { 1 + \sin ^ { 2 } n } { 5 ^ { n } }$ converges.

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Definitions:

Romanesque Feature

Architectural characteristics typical of the Romanesque style, including rounded arches, solid construction, and extensive use of stone.

Portals

Gateways, either real or symbolic, that connect two distinct areas or realms.

Amiens

A city in northern France, known for its Gothic Amiens Cathedral and its role in World War I and II history.

Rayonnant Style

An architectural style of Gothic architecture, noted for its elaborate decorative elements and emphasis on the play of light, prevalent in the 13th and 14th centuries.