Don't give this solution we find the value or interval for x and also discuss at end points Test for convergence the series3.6.9(i) En= 13n7.10.13...•..x" (x> 0),(3n + 4)0.2.4.6 ...(2n +2)3.5.7 ... (2n + 3)(ii) E(x>0). ) Let Š Une be thegivenseriesこuThenUn =3. 6.9.3 n7.10.13--(3nt4)Now,Unti3-6-9.... 3n. (3n+3)7.10.13. -(3n+y)un7.10. 13.3.6.9 - 3り- 3n+ 33n+7Un3n+7二unH3n +3also,'3n+73n+7- 3 n- 3Un-)ニUnti3n+33n +3こ3n+3n. 4: Lim n -1) = limn(3+ %)UnHLim* >13+ 3m: Theis convergent..seriesgiven

Answered: Image /qna-images/answer/0e646528-3bf2-40c4-addf-2bf01e9ac797.jpg

Answered: Test for convergence the series 3.6.9…

Test for convergence the series 3.6.9 ... 3n (i) E x" (x > 0), 7.10.13 ... (3n + 4) 2.4.6 ... (2n + 2) Σ 3.5.7... (2n + 3) メー' (x>0). (ii)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.5: Mathematical Induction

Problem 27E

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Question

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Don't give this solution we find the value or interval for x and also discuss at end points

Test for convergence the series
3.6.9
(i) E
n= 1
3n
7.10.13...
•..
x" (x> 0),
(3n + 4)
0.
2.4.6 ...
(2n +2)
3.5.7 ... (2n + 3)
(ii) E
(x>0).

) Let Š Une be the
given
series
こu
Then
Un =
3. 6.9.
3 n
7.10.13--(3nt4)
Now,
Unti
3-6-9.... 3n. (3n+3)
7.10.13. -(3n+y)
un
7.10. 13.
3.6.9 - 3り
- 3n+ 3
3n+7
Un
3n+7
二
unH
3n +3
also,
'3n+7
3n+7- 3 n- 3
Un
-)
ニ
Unti
3n+3
3n +3
こ
3n+3
n. 4
: Lim n -1) = lim
n(3+ %)
UnH
Lim
* >1
3+ 3m
: The
is convergent.
.
series
given

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