Suppose that an(x – 6)" converges for x = 10. At which of the points (a)-(d) must it also converge? (a) x = 8 (b) x = 11 (c) x = 3 (d) x = 0

Q: If 2a, converges, then 1. diverges Select one: True False

A: Use the defination of convergence of a series.

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: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

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

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Q: 20. Show that if E-1a, converges, then 1 + sin(a,) Σ n=1 converges.

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Q: 4. Find the interval of convergence E (2x+3)"

A: Here we have to find the interval of convergence ,  ∑n=0∞(2x+3)n

Q: Given that lim n2(x- 5)" converges by the Ratio test. If x€ Z then the numerical n- 00 value of x is…

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Q: What are all of the values of x ,such that Σ (3x)" (-1)"+ 00 converges? n=1

A: To solve this question we shall use root test for series.

Q: Examine the convergence of ,where a>1. (log x)" +1

A: First I have told about Improper integral of first kind and then using it evaluate the given…

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: Find the interval of convergence of Σ 6" (2n + 1)!

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Q: What are all of the values of x such that (-1)"+1 Σ (3)" converges?

A: The ratio test states that: if L < 1 then the series converges absolutely; if L > 1 then the…

Q: Find the interval of convergence : En-0 (x-3)"

A: Apply ratio test to find the interval of convergence. When L<1 then series converges and When…

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: (3n)" (2n + 50)" n=1

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Q: (b) Give an example to show that the product (fngn) may not converge uniformly.

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Q: Suppose that anx" converges for x = 5. Must it also converge for x = 4? What about x = -3?

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Q: 9. Determine by the root test if Ln=2 (4n-5\n 2n+1, converges or diverges.

A: Explained below

Q: 1 3 .5 4 X +x

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Q: Determine the interval and radius of convergence for E-1) (+1)*

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Q: (-1)"(х + 3)" Σ n2n n=1

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Q: 3. Determine whether E (-1)" converges absolutely, conditionally or diverges. Explain.

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

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Q: The interval of convergence of +∞ x2n Σ(-1)" is (2n)! n=0

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Q: Find the radius and interval of convergence for (-1)"(x – 1)" n4" n=1

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Q: If {fn}n=1 is a pointwise convergent, then {fn}=1 is uniformly convergent.

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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: What's the convergent of this problem?

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Q: 4n Determine whether {} 5n+1 is convergent or divergent.

A: A sequence {an} is convergent if limn→∞an=l, where l is a finite real number.A sequence {an} is…

Q: What are all of the values of x, such that converges?

A: We have to use GP sum Common Ratio.

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

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Q: Suppose that p(æ) > anx" converges on (-1, 1], find the internal of convergence of p(6x – 9). n=0

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Q: Find the interval of convergence for 3x+1 Σn(n+1)*

A: Given series is ∑n=1∞3nxn+1n(n+1)

Q: Find the interval of convergence of (3x)^n/(2n)!

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Q: 4n Determine whether Σ: 5n+1 is convergent or divergent.

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

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Q: (x – 3)" 2n +1 - Determine the interval of convergence of n=1

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Q: Find the radius of convergence of (-1)"x' 4n n=0

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Q: Find the interval of convergence of ∞∑n=0 ((-1)n (x+1)n )/ (2n).

A: We have to find the interval of convergence of the given series.

Q: 8) FIND THE INTERVAL OF CONVERGENCE FOR Σ (-1)" x 1=2 n2^ n

A: The given series: ∑n=2∞-1nxnn2nWe need to find the interval of convergence.

Q: Find a sequence X, such that it does not converge to any real number, but Y, does converge to some…

A: Consider the sequence Xn=(-1)n. Then Xn={-1,1,-1,1,-1,1,-1,1,...}. So, Xn does not converges to any…

Q: Find the values of p such that E(-1)"- converges.

A: The given series :

Q: 17. Find the interval of convergence for E(-1)"-1÷) x'

A: To find the interval of convergence.

Q: 2. Use the previous item to determine if the improper integ 2x – x3 d.x (x – 1)²(x² +1) 8∞ converges…

A: This is a problem of improper differential equation. First by partial fraction decomposition we will…

Q: Give an example of a sequence of continuous functions: fn : [0, 1] → R that has no pointwise…

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Q: 2" Зп+2 n=0

A: