Please show me the procedure/calculations (especially for the root test and where it converges) for this question. The results are already written but I would like to understand how to find these results. If not specified otherwise, fill in the blanks with integers (pos-sibly 0 or negative). A fraction should be reduced (for ex-ample, is accepted but not ), and if it is negative and theanswer boxes (such as 4) have ambiguity, the negative signbais acceptedshould be put on the numerator (for examplebut is not). log x = loger, not log10 .Let us study the following series E-0 (n+1)(4+1)with various x.5(x + 1)²,This series makes sense also for x C. For x = i√3, calculate(3-3)²aс5(x + 1)2nn=0 (n+1)(4+1)bda-62b 17 ✔C-96 ✓d:17 ✓In order to use the root test for a € R, we put an =1)2. Complete the formula.the partial sum -lim (a)n-xega+hjfor < x <kj: -5 ✓k: 3✔1:-1 ✔ m 3 ✔For the case x = -1, the seriesconverges absolutely. ✔converges but not absolutely.=e: 9f4g: 1 ✓h:1✔: 2 ✓Therefore, by the root test, the series converges absolutely1m• diverges.For the case r=-3, the series• converges absolutely.converges but not absolutely.• diverges. ✔√3i.(3-3)²(n+1)(4+1)(x+

Answered: Image /qna-images/answer/c0f643f2-4d22-48b4-a216-39d1740d9241.jpg

Answered: (3-3) Let us study the following series…

Math

Advanced Math

(3-3) Let us study the following series E-0 (n+1)(4+1)(x + 1)²,

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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Question

Please show me the procedure/calculations (especially for the root test and where it converges) for this question. The results are already written but I would like to understand how to find these results.

If not specified otherwise, fill in the blanks with integers (pos-
sibly 0 or negative). A fraction should be reduced (for ex-
ample, is accepted but not ), and if it is negative and the
answer boxes (such as 4) have ambiguity, the negative sign
b
a
is accepted
should be put on the numerator (for example
but is not). log x = loger, not log10 .
Let us study the following series E-0 (n+1)(4+1)
with various x.
5(x + 1)²,
This series makes sense also for x C. For x = i√3, calculate
(3-3)²
a
с
5(x + 1)2n
n=0 (n+1)(4+1)
b
d
a
-62b 17 ✔C-96 ✓d:
17 ✓
In order to use the root test for a € R, we put an =
1)2. Complete the formula.
the partial sum -
lim (a)
n-x
e
ga+h
j
for < x <
k
j: -5 ✓k: 3✔1:-1 ✔ m 3 ✔
For the case x = -1, the series
converges absolutely. ✔
converges but not absolutely.
=
e: 9f4g: 1 ✓h:1✔: 2 ✓
Therefore, by the root test, the series converges absolutely
1
m
• diverges.
For the case r=-3, the series
• converges absolutely.
converges but not absolutely.
• diverges. ✔
√3i.
(3-3)²
(n+1)(4+1)(x+

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