Questions
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Which of the following statements is NOT true?
Options
A.a. A series with infinitely many positive terms and finitely many negative terms is usually conditionally convergent.
B.b. A series can only be conditionally convergent if it has infinitely many positive terms and infinitely many negative terms.
C.c. The series [math: 1−1/3+1/5−1/7+⋯]1-1/3+1/5-1/7+\cdots is conditionally convergent.
D.d. We can make a conditionally convergent series into a divergent series by changing the signs of infinitely many of its terms.
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The question asks to identify which statement is NOT true, so I will examine each option for accuracy and common misconceptions.
Option a: 'A series with infinitely many positive terms and finitely many negative terms is usually conditionally convergent.' Here, if there are only finitely many negative terms, the tail of the series consists of positive terms alone. If the positive terms do not sum to a finite limit, the series cannot converge, and even if the positive terms do converge, adding finitely many negative terms ......Login to view full explanationLog in for full answers
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