- 1)n+'] (a) Converges to Diverges .......... 5"

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: Show that the series Ln=l 12+2z10n-5z"ª –3z+2;10n converges absolutely for |리 < 1.

A: The series ∑n=1∞an is absolutely convergent if the series ∑n=1∞an  Ratio test:  The series ∑n=1∞an…

Q: - Find the interval of convergent for : 2n 2 2n! n=0

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Q: How would I find if the sequences an=nπ cos(nπ) and an= (n2)(1/n) are convergent/divergent?

A: To examine the given sequence regarding convergence, that is study the limits as n tends to infinity

Q: Find an infinite series that converges to 1/2 ex - 1 dx.

A: Consider the integral: I=∫012ex-1xdx……1

Q: 8. Determine by the ratio test if 2n=1 (2n)! converges or diverges.

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Q: Find the interval of convergence of the series. (3x)" 2" n=1

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Q: 3 Show that the (sn} sequence given in general terms converges. Sn + n+2 n+1 2n +

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Q: What is the convergent of this problem?

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Q: Find the interval of convergence of the series. Σ (x-1)n (5n)! n=1 -119 sxs 121 xS2 -00 <x< 00 0sxs2

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Q: (-1)ªn n² + 1 mula converges to a value or diverges withou

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Q: Sn(x) = e-(2-n)a

A: Given that, fnx=e-x-n2 To show that the given function is uniform convergence at [-1,1]. Let,…

Q: N! 9) Show that converges/diverges

A: Use D Alembert ratio test

Q: Find the interval of convergence of the series Ex-1 k=1 k3 *

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Q: 7N 8N 3) Show that converges/diverges.

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Q: Does the series of n=1 to infinity of (-1)^n*sin(9/n) converge or diverge?

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Q: The sequence (n+(-1)" n Diverges Converges to 0 Converges to 1 Converges to e Converges to 2e

A: Option 3 is correct.

Q: cos NII 2) Show that converges/diverges.

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Q: 1 n4 + sin“ n=1

A: To find that the given deries diverges or converges

Q: The sequence {()} Sn+3 Sn+1 n-1 converges to e converges fo te ConvCrges fe Ve Converges 00 Diverges

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Q: The series 2=1 1 k is divergent no conclusion absolutely convergent conditionally convergent

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Q: converges or diverges. I-

A: We have to find out the given series is convergent or divergent. If the series is convergent then we…

Q: 9. Estimate the value of the convergent series 8 k=1 (-1)^² k! + 2k with an absolute error less than…

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Q: What is the function represented by the power series from k=0 to infinity of ((-1)^k*x^(k+1))/4^k?

A: Power series

Q: A sequence of functions that converges pointwise on [0, ∞0) but does not converge uniformly [0, 0).…

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Q: N 2N + 1 2) Show that converges/diverges. +

A: We have to show whether the series converges or diverges.

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

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Q: Vn +1- n –1 n=1

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Q: Does the series from 1 to infinity of 1/(3^k-2^k) converge or diverge using the limit comparison…

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Q: What is the function represented by the power series from k=0 to infinity of (-1)^k(x^k)/(3^k)?

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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: Find the interval of convergence of the series (–1)"(x+3)*+1 п(п + 1) n=1

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Q: How do I determine if this converges to a certain value, or diverges without bound?

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

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

A: Ratio test

Q: 2. If Exn and E yn are convergent. Show that E(xn + Yn) is convergent.

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Q: The series 3 k 1 3. is 3. convergent to O None divergent convergent to 3 convergent to

A: We have to solve

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: (1) Show that n2 +1 n=1 converges conditionally. Show that all conditions of the test used are…

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Q: Use comparison test to show that the series E=1 (2) converges. 5n2-п.

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Q: N + 1 2N 2) Show that converges/diverges. N-1

A: The given series is: ∑N=1∞N+12N+1 Let. aN=N+12N+1,N≥1

Q: 4. If > Cn (T + 2)" converges for -5 < x < 1, find the radius of convergence of the series. n=1

A: The given power series is cn(x+2)n , n from 1 to infinity.

Q: 4. Show that the sequence {fn}, where nx fn(x)=- xER 1+n°x' is point-wise convergent but is not…

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Q: 1. Show that the sequence ((nx - - 1/n)e n) converges uniformly on [0, 0). (15 points)

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Q: 5. Show that the sequence Pn = 1 converges linearly to p 0, and the sequence Pn = 10-2" converges…

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Q: A function can be represented by its Taylor Series only on its interval of convergence. True False

A: True

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

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