Give an example of two convergent series E1 *k and E1 Yk such that = *kYk diverges. Can this happen if one of the series is absolutely convergent?

Q: 1. Give an example of a series such that > an converges but > an| diverges.

A: To give an example for: ∑an converges but ∑ an diverges.

Q: Find the radius and interval of convergence of the power series: >7"(10x – 1)" n=0

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Q: Find the interval of convergence of the series. 7x" Σ n = 1

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Q: (x-4)" 6" n n=1 IM

A: See the detailed solution below.

Q: Find the interval of convergence and radius of convergence of the following power series. E(-1)" 2n…

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Q: Find an example of two sequences (an)neN and (bn)neN such that both sequences Ei=19 and ₁=1b;…

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Q: 19. Give an example of divergent series E ak and E, bu such that the series E akbk converges.

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Q: Find the sum of the convergent series. 1 (n + 1)(n + 2)

A: To expand the summation, split the given summation into the summation of two series.…

Q: 1 (Kn)! संपो हे

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Q: Suppose that the nth partial sum of a series (∑∞n=1  an) is sn = (n+1) /( n+2). Is the series…

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Q: (-1)"(х + 3)" Σ n2n n=1

A: Topic:- convergence of a series

Q: If a geometric series converges to a / (1-r) if |r| < 1, the interval of convergence is

A: If a geometric series converges to a1-r ,  if |r|&lt;1 { Given }

Q: Find the sum of the following convergent series: [tan(2n – 1) – tan-(2n + 3)]. n=0

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Q: assume that |an+1/an| converges to ρ = 1/3 . What can you say about the convergence of the given…

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Q: Find the smallest value of x for which the series Σ (x+101)" 2ln(n) n=2 is conditionally convergent.

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Q: Find the interval of convergence for the power series (x – 3)" n6 + 8 n=0

A: We know by Ratio Test, the series ∑an is convergent if limn→∞an+1an &lt; 1.

Q: Find the interval of convergence for the series E- nx" in=D

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Q: Find the radius and interval of convergence of the power series 】 (−1)” (x+3)” √2n n=1

A: This is a problem related to series and sum calculation. Please follow the procedure given below.

Q: The series E² is convergent and has a sum.

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Q: Give an example of two series E an and Ebn, both convergent,such that anbn diverges.

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Q: Verify that the infinite series diverges.

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Q: Find the first five non-zero terms of power series representation centered at x = O for the function…

A: We have to find power series representation of  f(x) = ln(3-x).

Q: 1 1 + 2y2 1 1 + 4V4 + 3/3 5V5 +

A: We will test the convergence of given sequence by using p-series test as shown below

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: Determine whether the series E, (-1)"-1 is convergent o n4 divergent.

A: By using ratio test of series

Q: Suppose that the power series ) Cn(x – 1)" converges when x = -2 and diverges when n=0 x = 6. (a)…

A: The power series ∑n=0∞cnx-1n converges when x = -2 and diverges when x = 6. We have to find the…

Q: The series E,= is convergent. Select one: O True O False

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Q: If given 1 1 1 1 +... determine whether the given series convergent or divergent ---+ 3 6 9 12 using…

A: Here we have to use the ratio test for checking the convergence of series

Q: Use any method to determine whether the series converges or diverges. Σ k + 1 k=1

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Q: C) ) Suppose Arat E Cn (x-2)" comverges when x-4 and diverges when x:6. Does the Power Series…

A: It converges at X=1

Q: Estimate the value of the following convergent series with an absolute error less than 10 - 3 Σ…

A: Given

Q: 2. Consider that > (x – 2)* is a geometric series. As such, for what values of x will this infinite…

A: Given that ∑k=0∞x-2kTo find : Value of xSolution :∑k=0∞x-2kRatio test ak=x-2k…

Q: Suppose that E Cn x" is a power series with interval of convergence (-3, 3) and that Cn a" converges…

A: There is no change in the interval of convergence of a series if we multiply is by a polynomial.…

Q: Find the sum of the following convergent series: Eltan-(2n – 1) – tan(2n + 3)]. n=0

A: Given series ∑n=0∞tan-12n-1-tan-12n+3 Assume ∑n=0∞tan-12n-1-tan-12n+3=∑n=0∞an-∑n=0∞bn Where…

Q: Find the sum of the convergent series by using a well-known fühct 2n (-1)" + 1 3 n n=D1

A: Given : ∑n=1∞-1n+12n3n nln1+x = ∑n=1∞-1n+1 xnn    as x &lt; 1Therefore,23 &lt; 1ln1+23 = ∑n=1∞-1n+1…

Q: Determine whether the alternating series converges. Σ k + 1 7k + 1 k=1

A: ∑k=1∞(-1)k+1k+17k+1  Above Series is an alternating seriesApply Liebnitz Testlet   ak=k+17k+1…

Q: If E an is a convergent series with positive terms, is it true that the series ( a) Σ(1+ α) (b)…

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Q: n3n n=1 IM:

A: The series converges if, lim(n→∞) |an+1/an|&lt;1

Q: the root test fails to determine if the series Σ (1 + n= 1 converges or diverges

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Q: Find the interval and radius of convergence of the power series k -(x – 2)* 42k 1 k 1

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Q: Expand the function e-2z f(z) = %3D - in the power series by the powers of z and indicate the…

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Q: Find the sum of the convergent series. Σ n(n + 2) W

A: First we rewrite the series and then find the sum.

Q: п En-)" sin (-1)" 2

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Q: If Ea, is a convergent series of positive terms, prove that Esin (a„) converges.

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Q: assume that |an+1/an| converges to ρ = 1/3 . What can you say about the convergence of the given…

A: The given series an is convergent.   Consider the series where all the terms of the series are non…

Q: (T)

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Q: Find the sum of the following convergent series: Eitan-(2n – 1) – tan-(2n + 3)]. n=0

A: Telescoping series and test for converges

Q: If a power series in (x – 4) converges when x = 11, then it must also converge when x = -2. |

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Q: Consider series E-1 an 00 n=1

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