Let a, = 2n+1– 2". Then, lim an %3D n-00 None of the other options the above co and the sequence (a,} is divergent the above 0 and the sequence convergent K

Q: Find all the values of a > 0 such that the given series (Зх — 0.4)* - k2 k=1 is convergent from x =…

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. 00 (-2)" Σ n2 n = 1…

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Q: 5n 9. Use the L'Hopital's rule to determine if the sequence an = () converges or diverges as limit n…

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Q: 3. Show that the series In 2+ (-1)k-1 -(x – 2)* k2k k=1 from Example 3 diverges when x = 0 and…

A: The given series is ∑an = ln 2 + ∑k=1∞(-1)k-1k. 2kx-2k.Putting x = 0, the series reduces to ∑an = ln…

Q: If gan converges and Σbn diverges, can anything be said about their term-by-term sum Σ(an + bn)?…

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Q: Determine whether the sequence 2ñ sin converges or diverges. If it con its limit. 27 1 1 2 diverges

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Q: How to determine nln(n)/(n+1)^3 is convergent or divergent?

A: To determine the sum of the series nln(n)/(n+1)^3 is convergent or divergent. Now, Apply the…

Q: 1 B. Find out if b, where b, = n* sin" 2en -Converges or, -Diverges (Show complete solution using…

A: Given the series is bn=n4sinn12en. Determine whether the series is converges or diverges.

Q: +o0 (-1)*n" sin" () Σ 2n n=1

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Q: (п +5)(п — 3) 1 | converges. If so, find its limit. n-1 Determine whether the sequence 4n?

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Q: Determine whether the sequence converges or diverges. If it converges, find its limit:

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Q: +oo Σ 8n2 16n + 6

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Q: Use divergence test to show that the series E-1(1 +-) 2%3D1

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Q: 1 is convergent, and find its sum. Show that the series n(n + 1) n=1

A: we have to show that the given series is convergent and then we have to find the sum. ∑n=1∞1n(n+1)

Q: Using the nth term test for divergence, the series n=1 n=1 is divergent since lim an n→ +0o

A: We have to use divergence test.

Q: Determine whether the sequence converges or diverges. 4n7t an = tan 3 + 16n lim an = DNE - 00

A: A sequence is called convergent if there is a real number that is the limit of the sequence. ... A…

Q: For each n E N= {1,2,3, ..}, define an (A)-cOs (규1). = COS COS n+1 1. Determine whether the sequence…

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Q: Compute the limit of the nth term and use it to explain why the series is divergent. +00 2" – 1 2 2n…

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Q: 10 The series n+10 Cannot be evaluated. Diverges Converges absolutely Corivergas conditionally

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Q: The series Lk = 1 (-1)*+1 is 2k divergent absolutely convergent conditionally convergent none

A: First I have written a short note about Absolutely and Conditionally convergent series and find tha…

Q: If the lim, (1+)" =e, then the series a, is (i) Converge (i) Diverge (ii) Inconclusive (1)

A: we have given that limn→∞1+1nn=e

Q: 42n (x + 6)" is convergent if The given power series : 9n

A: solve the following

Q: 2 n 1 o Show that + converges/diverges n-

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Q: +00 n! と+1 n=1

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Q: Suppose SELECT an A) lim B) a, converges --(-) (-1)" an= 1+ C) according to LCT both series, a, and…

A: Explanation of the answer is as follows

Q: Write power series of f(x) = 3 about x = 0. %3D 1- 4.r

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Q: B. Find out if E bn where bn = n* sin" -Converges or, 2en -Diverges (Show complete solution using…

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Q: Give a power series Cnx" such that it is =1 convergent if |x| l of x = -1.

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Q: Show that the series n' (2n)! is convergent. Deduce that lim (2n)! n=1

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Q: Find the interval of convergence of the Taylor series of the function f(x)= in powers of (x- 1). 3-X…

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Q: 11. For each x,, Show that x, (-1)"x, converge or diverge. n=1 n=1 (*Using comparison test and…

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Q: Find the limit of the sequence if it converges; otherwise indicate divergence. tan-1 n 1) an

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Q: 4. Determine if the sequence (sin²n+ 2n converges or diverges. Find the limit if it converges.

A: we have to identify the given sequence is convergent or divergent if convergent then find it's limit

Q: Find the sum of the convergent series tan - ( m til tan M=1

A: This is a telescoping series.  Whose sum is  2/π

Q: 2. If the power series defined by En=1 an (x + 1)" converges at x=3, thenE-1(-1)" an…

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Q: a n+1 =1 then the series is Suppose lim 71 Divergent Convergent Analytic inconclusive

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Q: 1 x converges 1 ex - e-X Select one: True False

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Q: If an converge to zero then the series -0 an is convergente Select one: True False

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Q: Σ converges/diverges N! 9) Show that

A: Ratio test

Q: Suppose that p(x)=an" converges on (-1, 1], find the interval of convergen n=0 8 left end included…

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Q: If a power series Cn(x + 2)" converges absolutely when x = 4, then i %3D

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Q: The series 2n +2 Diverges to-o0 Converges to 1- Converges to B Diverges to +

A: Given series is ∑n=1∞sinπ2n-sinπ2n+2 The Nth partial sum of given series is…

Q: Determine whether the sequenceconverges or diverges. If it converges, find its limit. an = cos2n/4n

A: Consider the given sequence. an=cos2n4n A sequence is said to be absolutely convergent. If an is…

Q: Determine whether the sequence converges or diverges. If it converges, find its limit:

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Q: Use Taylor series to evaluate the limit. lim x -4 -1 O 4

A: Given: limx→∞x2e4x2-1 ....(1) From Taylor's series we have e4x2=1+4x2+124x22+164x23+...…

Q: Use the Ratio Test to determine whether the series is converge Σ (-6)" (2n + 1)! n = 0 Identify an.…

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Q: Let fn(x) be the following sequence (not series) of functions n2 fn(x) = (x2 + 7x + 6)n² +n

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Q: The sequence fn(x) = is 72 Select one: a. diverges Ob. converges uniformly but not pointwise C.…

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Q: Show that the series n" (2n)! is convergent. Deduce that lim 0. (2n)! n=1

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