Let , be a series with partial sums Sy. If a-fn), where f(x) Time ieft continuous, and decreasing function. Which of the following statements are always true? LIH E, converges, then lim a,- 0. IL. E,- L., then lim a, -L. III. H lim a, - 0, then E converges. IV. lim Sy - L then , - L. V. rada - L, then . -L. A) III and IV. C B) II, III, IV. C) I and IV. D) III, IV, V. Allof them

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 82E
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IMG 6657.JPG
Let Ea, be a series with partial sums Sy. If an - f(n), where f(x) Time ieft 0:19:08
continuous, and decreasing function. Which of the following statements are always true?
L If E1, converges, then lim a,- 0.
II. IH E,- L, then lim a, - L.
III. H lim a, - 0, then E
2 . converges.
IV. If lim Sy - L, then E1 - L.
V. If, rx)dx - L, then E.- L.
A) III and IV.
C
B) II, III, IV.
C)
I and IV.
D) III, IV, V.
Allof them
Transcribed Image Text:4:31 1 Telegram IMG 6657.JPG Let Ea, be a series with partial sums Sy. If an - f(n), where f(x) Time ieft 0:19:08 continuous, and decreasing function. Which of the following statements are always true? L If E1, converges, then lim a,- 0. II. IH E,- L, then lim a, - L. III. H lim a, - 0, then E 2 . converges. IV. If lim Sy - L, then E1 - L. V. If, rx)dx - L, then E.- L. A) III and IV. C B) II, III, IV. C) I and IV. D) III, IV, V. Allof them
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