If $\sum _ { n = 1 } ^ { \infty } c _ { n } x ^ { n }$

question 96

Essay

If $\sum _ { n = 1 } ^ { \infty } c _ { n } x ^ { n }$ is convergent at $x = 3$ , what can be said about the convergence or divergence of the following series?
(a) $\sum _ { n = 1 } ^ { \infty } c _ { n } 4 ^ { n }$ (b) $\sum _ { n = 1 } ^ { \infty } c _ { n } ( - 2 ) ^ { n }$ (c) $\sum _ { n = 1 } ^ { \infty } c _ { n } ( - 3 ) ^ { n }$

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Definitions:

Defense Mechanisms

Protective strategies unconsciously applied to avoid the discomfort arising from thoughts or feelings that are not acceptable.

Id Impulses

The instinctive and primitive behaviors and urges that are derived from the id part of the psyche, according to Freudian theory.

Superego

In psychoanalytic theory, the part of the personality responsible for ideals, moral standards, and conscience.