Determine the Convergence or Divergence of the Series $\sum _ { n = 1 } ^ { \infty } \frac { 6 ^ { n } } { 900 }$

question 90

Multiple Choice

Determine the convergence or divergence of the series $\sum _ { n = 1 } ^ { \infty } \frac { 6 ^ { n } } { 900 }$ . Use a symbolic algebra utility to verify your result.

• A)The series converges.
• B)The series diverges.

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Definitions:

Avignon Papacy

The period from 1309 to 1377 during which seven successive popes resided in Avignon, France, rather than in Rome, leading to a significant schism in the Catholic Church.

Great Schism

Refers to two major divisions in Christian history; the first in 1054 between the Eastern (Orthodox) and Western (Catholic) Churches, and the second, beginning in 1378, a division within the Roman Catholic Church where rival popes were established.

Conciliar Movement

A reform movement in the medieval Christian Church aiming to resolve papal disputes by convening authoritative councils, asserting that such councils held supremacy over the Pope.

Reformation in England

The series of events in the 16th century when the Church of England broke away from the authority of the Pope and the Roman Catholic Church.