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(g) For each fixed k, and each a such that 0 < a < 1, the series Enka" converges and thus, lim na" = 0 (h) Suppose that fn(z)| ≤ M₁ for ne N where (M) is a sequence of positive numbers. Then, the series Ef. (r) con- verges uniformly when M,, converges.

(g) For each fixed k, and each a such that 0 < a < 1, the series Enka" converges and thus, lim na" = 0 (h) Suppose that fn(z)| ≤ M₁ for ne N where (M) is a sequence of positive numbers. Then, the series Ef. (r) con- verges uniformly when M,, converges.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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Modified true or false. If it is false, give a counterexample and briefly explain. If true, give a short proof.

(g) For each fixed k, and each a such that 0 < a < 1, the series Enka" converges and thus, lim na"=0 (h) Suppose that fn(2)| ≤ Mn for ne N where (M) is a sequence of positive numbers. Then, the series Ef. (r) con- verges uniformly when M,, converges.
Transcribed Image Text:(g) For each fixed k, and each a such that 0 < a < 1, the series Enka" converges and thus, lim na"=0 (h) Suppose that fn(2)| ≤ Mn for ne N where (M) is a sequence of positive numbers. Then, the series Ef. (r) con- verges uniformly when M,, converges.
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