Consider the series 8m (qn)8 n=1 An n=1 n7" +6 To determine whether this series converges, it is convenient to use the ratio test. Using this test, we can express the quotient an+1/an of any two subsequent terms in the form where a = 8 The series will converge for g <1 8 ag. (b+ =) * . n7" +6 (n + 1) 7"+1 +6 b=1 and c 1 Finally, we want to check whether the series converges with q at the upper bound of this range (since the test we just applied is inconclusive there). We compare with the p-series Σn=-1 1 bn = K NP ' bn, where with K is a constant and p -7 identified the series is "d" , and so when g is equal to the upper bound previously (type "c" or "d" for convergent or divergent, respectively).
Consider the series 8m (qn)8 n=1 An n=1 n7" +6 To determine whether this series converges, it is convenient to use the ratio test. Using this test, we can express the quotient an+1/an of any two subsequent terms in the form where a = 8 The series will converge for g <1 8 ag. (b+ =) * . n7" +6 (n + 1) 7"+1 +6 b=1 and c 1 Finally, we want to check whether the series converges with q at the upper bound of this range (since the test we just applied is inconclusive there). We compare with the p-series Σn=-1 1 bn = K NP ' bn, where with K is a constant and p -7 identified the series is "d" , and so when g is equal to the upper bound previously (type "c" or "d" for convergent or divergent, respectively).
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:Consider the series
8m (qn)8
n=1
An
n=1
n7" +6
To determine whether this series converges, it is convenient to use the ratio test. Using this test, we can express the
quotient an+1/an of any two subsequent terms in the form
where a = 8
The series will converge for g <1
8
ag.
(b+ =) *
.
n7" +6
(n + 1) 7"+1 +6
b=1
and c 1
Finally, we want to check whether the series converges with q at the upper bound of this range (since the test we just
applied is inconclusive there). We compare with the p-series Σn=-1
1
bn
= K
NP
'
bn, where
with K is a constant and p
-7
identified the series is "d"
, and so when g is equal to the upper bound previously
(type "c" or "d" for convergent or divergent, respectively).
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