a) Find A and B such that(12)*(4*+1_3k+1)(4* _3k)3k A4k_3k3kB4k+1_3k+1b) Use the result in part a) to find a closed form of the nth partialsum of the series(12)*k=1 (4k+1_gk+1)(4*_3*)and then find the sum of the series.(12)*(4*+1_3k+1)(4* –3k)3k A+4k+1_3k+13* BTürkçe: a)%3D4k – 3kolacak şekilde A ve B değerlerini bulunuz.b) a)'daki ifadeyi kullanarak önce aşağıdaki serinin n'inci kısmitoplamını, sonra da serinin toplamını bulunuz:(12)*Lik=1 (4k+1_3k+1)(4* –3*)ОА- 1, В- —3, S, — 3 —3"+14"+1_3n+1,Sum = 3O A= 3, B = -1, S, = 337+147+1_3n+1 >Sum = 3%3D6.O A= 1, B = -3, S, = 4 –3+147+1_3n+1Sum = 4%3DO A= 3, B = -1, S, = 3 -3"Sum = 3%3D4" -3" )37ОА-3, В — — 1, S, — 4Sum = 4%3D%3D

Answered: Image /qna-images/answer/4a33fe99-395b-4eb4-855f-25241e6fa8b9.jpg

a) Find A and B such that (12)* (4*+1_3k+1)(4* _3k) 3k A 4k_3k 3kB 4k+1_3k+1 b) Use the result in part a) to find a closed form of the nth partial sum of the series (12)* Ek-1 (ak+1_gki1)(4*_3*) and then find the sum of the series.

a) Find A and B such that (12)* (4+1_3k+1)(4 _3k) 3k A 4k_3k 3kB 4k+1_3k+1 b) Use the result in part a) to find a closed form of the nth partial sum of the series (12)* Ek-1 (ak+1_gki1)(4_3) and then find the sum of the series.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 72E

See similar textbooks

Related questions

Q: Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to…

A: In the question it is asked to approximate the sum of series with an error of less than 0.001.

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper…

A: Here we have to find out the convergence of The infinite series and then we find out the sum if it…

Q: 1 Determine whether the infinite series is Convergent or Divergent. n(Inn)

Q: 8.8.8. Use a known Taylor series to conjecture the value of the limit.

A: We simply plug in the Taylor series for the sinx.Formula used:

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an…

Q: 4. (a) Determine whether the geometric series 0.12+0.0012+0.000012 + . - is convergent or divergent,…

A: The given series0.12+0.0012+0.000012+......

Q: 9. Determine convergence or divergence of the series. k=1

Q: 1. (a) Use Root Test to determine whether the series 2n en converges absolutely, conditionally, or…

Q: Show that the series E (-1)"-'bn, where b, = 1/n if n is odd and bn 1/n if n is even, is divergent.…

A: According to the given information, it is required to show that:

Q: Σ 1 converges or diverges. Determine whether the series 4 k+ 2

A: Given that, ∑f(x) = ∑ 14k+2 for convergence and divergence first…

Q: Find Taylor Series generated by 3* at a=1.

A: To find a taylor series generated by 3^x at a=1

Q: Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to…

A: According to the Alternate series Remainder Theorem: The remainder Rn=s-sn≤an+1, if sn is sum of…

Q: Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to…

Q: 2. (16pts.) If the Nth partial sum sequence sy = an = 3 - then determine whether the N +1' n=0…

A: To find whether series is convergent.

Q: Express the series using sigma notation 5-10 + 20-40+80 °5(-2)-¹ 21 -2n-5 7-1 0-5(-2)-1 -2(5)-¹ 7-1…

A: Infinite series

Q: (a) Find at least 10 partial sums of the series using Excel. Compute the first three partial sums…

A: The given series is ∑n=1∞ cos n a) Partial sum using excel : n cos n Sn partial sum 1…

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper…

Q: [9]. Suppose that a ball is dropped from an initial height of 300 feet, and subsequently bounces…

A: The initial fall h=300 The first rise & fall 2*.9× 300 The 2nd rise & fall…

Q: 2. Determine if each series converges or diverges, you can use any of the tests discussed in class.…

A: Consider the series ∑n=1∞n3n−2

Q: 8. State the alternating series test. As well, suppose the sequence {ak}=o is decreasing and ak > 0…

A: Here we have to state the alternating series test. And suppose the sequence akk=1∞ is decreasing…

Q: Use the alternating series remainder theorem to determine the smallest number of terms for require…

Q: The series with the expansion +(z-)(2-)* - -)° +... is a Taylor series. Select the correct answer…

A: I have written summation form of possible series that is not same the given series si given…

Q: 2k converges or diverges. Determine whether the series >, 10k +7 a) Oconverges b) Odiverges c)…

Q: Use standard Maclaurin Series to find the series expansion of f(x) = 5et* In(1 + 8x). a) Enter the…

A: Cauchy product of two power series converges in the common region of two regions of convergence.

Q: 9 Determine whether the series 9. 9. +...+ 9. +... is convergent or 100 1002 1003 100" divergent. If…

A: 9100+91002+91003+.....+9100n+...common ratio:a2a1=a3a2=1100First term: a=9100common ratio:…

Q: Determine whether the series converges using the Ratio test. The series IM8 k= &

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

Q: Use an appropriate Taylor series to find the first four nonzero terms of an infinite series that is…

Q: Find a power series representation of 1/7-x centered at 0.

A: Consider the function To find- the power series representation of f(x) centered at 0.

Q: Write the first five terms (or the series in summation notation) of the Taylor series for 2x2 /…

Q: Write a Taylor series for In(4 + 2x) centered around x-0. Please write the series in summation…

A: Taylor series

Q: Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to…

A: The given data is: ∑n=1∞-1n+15n3-3 To use the alternative series remainder theorem to determine the…

Q: Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to…

Q: 2. Apply the Remainders in Alternating Series Theorem 5.14 to determine N, the number of terms…

A: The given alternating series is ∑n=1∞-3n7nn!. We need to find the number of terms required to…

Q: differentiate the maclaurin series 1/(1-6x) twice to find the maclaurin series of 1/((1-6x)^3).…

A: The objective here is to find the maclaurin series of 11−6x3

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper…

A: Use geometric series test to solve given problem.

Q: Use an appropriate Taylor series to find the first four nonzero terms of an infinite series that is…

Q: Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to…

A: According to alternating series remainder theorem, the approximation error of the summation of first…

Q: Use the Alternating Series Remainder Theorem to determine the number of terms required to…

Q: 4) Express the series in summation notation using its general term. Then, identify the function…

Q: 6. If a series Lu, converges to the sum u then so does any series obtained from Lun grouping the…

Q: 6. Use the definition of Maclaurin series to find the first four nonzero terms of the Maclaurin…

Q: (a) Find the total length of the intervals removed from [0, 1] after three iterations, i.e. the…

A: (A) given interval in the starting I0=0,1 then removed the interval 13,23 that is, length removed at…

Q: The Ratio Test involves a sequence {ar} such that ar +0 for all k and l = lim ak+1| Show that The…

Q: Use any method to find the Maclaurin series written in summation notation for f(x)= xsin(x)

Q: The terms of a series are defined recursively by the equations az = 5 5n + 2. an. an+1 4n + 11…

A: Here, the given series has: a1=5, an+1=5n+24n+11an

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper…

Q: 2) Determine the Maclaurin Series expansion in summation form for f (x)= cos( os (x²) . You may use…

A: We have to find maclaurin series.

Q: (a) Find the total length of the intervals removed from [0, 1] after three iterations, i.e. the…

A: This is a problem of Cantor set.

Q: 5. Use the definition of the Taylor Series to find the Taylor Series for the function f(a) 2- cos(x)…

Question

a) Find A and B such that
(12)*
(4*+1_3k+1)(4* _3k)
3k A
4k_3k
3kB
4k+1_3k+1
b) Use the result in part a) to find a closed form of the nth partial
sum of the series
(12)*
k=1 (4k+1_gk+1)(4*_3*)
and then find the sum of the series.
(12)*
(4*+1_3k+1)(4* –3k)
3k A
+
4k+1_3k+1
3* B
Türkçe: a)
%3D
4k – 3k
olacak şekilde A ve B değerlerini bulunuz.
b) a)'daki ifadeyi kullanarak önce aşağıdaki serinin n'inci kısmi
toplamını, sonra da serinin toplamını bulunuz:
(12)*
Lik=1 (4k+1_3k+1)(4* –3*)
ОА- 1, В- —3, S, — 3 —
3"+1
4"+1_3n+1
,Sum = 3
O A= 3, B = -1, S, = 3
37+1
47+1_3n+1 >
Sum = 3
%3D
6.
O A= 1, B = -3, S, = 4 –
3+1
47+1_3n+1
Sum = 4
%3D
O A= 3, B = -1, S, = 3 -
3"
Sum = 3
%3D
4" -3" )
37
ОА-3, В — — 1, S, — 4
Sum = 4
%3D
%3D

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Power Series$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.