21. Which of the following statements about series is false? (A) u, u =uz , where m is any positive integer. %3D k=1 k=m (B) If u, converges, so does cu, if c#0. ( C) r Σα, and Σ converge, so does (ca, + b,), where c # 0. (D) If 1000 terms are added to a convergent series, the new series also converges. (E) Rearranging the terms of a positive convergent series will not affect its conver- gence or its sum.
21. Which of the following statements about series is false? (A) u, u =uz , where m is any positive integer. %3D k=1 k=m (B) If u, converges, so does cu, if c#0. ( C) r Σα, and Σ converge, so does (ca, + b,), where c # 0. (D) If 1000 terms are added to a convergent series, the new series also converges. (E) Rearranging the terms of a positive convergent series will not affect its conver- gence or its sum.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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#21. See attached image for question
Transcribed Image Text:21.
Which of the following statements about series is false?
(A) >u, = u, , where m is any positive integer.
k=1
k=m
(B) If >u, converges, so does >,cu, if c + 0.
(C) If >a, and > b, converge, so does>(ca, + b,), where c + 0.
(D) If 1000 terms are added to a convergent series, the new series also converges.
(E) Rearranging the terms of a positive convergent series will not affect its conver-
gence or its sum.
8.
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