Show that 2"x" converges if |x| <. n=1

Q: |an also converges because 0 If an converges then < lan|, for n = 1, 2, ... n=1 n=1

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Q: 3. Suppose {fa) is an equicontinuous sequence of functions on a compact set K, and U.) converges…

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Q: oblem 3. Use the integral test to determine whether Y converges or diverges.

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Q: Determine whether the given converges or diverges. n Σ 2n + 1 n=1

A: Given is a series ∑n=1∞n2n+1n To check if the given series is convergent or divergent Ratio test:…

Q: 00 Show that converges if [r| < 1. п: п

A: The given series is

Q: 5. Find all values of x >0 so that ) converges. 3k k=2

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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: 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: N! 9) Show that converges/diverges

A: Use D Alembert ratio test

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

A: The ratio test states that: if L &lt; 1 then the series converges absolutely; if L &gt; 1 then the…

Q: Show that > iP converges to a finite value iff p < –1. i=1

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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: Find all values of x such that converges. n! n=1

A: Given that, series ∑n =1∞  xn2n! Compare the series ∑n =1∞  xn2n! with its standard form ∑n =1∞  an…

Q: +o0 (-1)*n" sin" () Σ 2n n=1

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Q: Indicate if the following statement is TRUE or FALSE. Briefly justify your response with an…

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Q: Find all values of x such that ΣΗ converges. n! n=1

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Q: Let {fn(x)} : „x ER and > 0. 1+ nx Show that ift>0, the sequence {fn(x)} converges uniformly on

A: Given: To explain the given statement as follows, To show that if t&gt;0, the sequence fnx converges…

Q: Suppose a,>0 for all n and 2 a, converges , which of the following must converge n = 1

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Q: an Show that if lim =0 and E-i b, converges then En=1 converges too. an =1 n+ 00

A: Given that  limn→∞anbn=0  and  ∑n=1∞bn converges.

Q: What are all of the values of x ,such that (-1)*+(n) * converges? (). x1.40

A: Using ratio test a series converges iff:…

Q: What are all of the values of x ,such that - (-1) n+A converges? n=1 .1 X26 .2 06

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Q: ? 4. Show that the sequence {fn}, where nx fn(x) = XER 1+n²x²⁹ is point-wise convergent but is not…

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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: Test the convergency o f Stan ("

A: According to the given information, it is required to test the convergence.

Q: . Find all values of x for which пх" n=1 (n + 1)(2x + 1)" converges absolutely.

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Q: (A) True (B) False The sequence {x}, where xn = 20" n! is convergent. :

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Q: Show that the sequence {fn} where fu(r) = e-n* is uniformly convergent on [a, b), a > 0.

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Q: Determine whether the given converges or diverges. n 2n +1 n=1

A: We can solve this as follows:

Q: Are there any values of x for which E=1(1/nx) converges? Give reasons for your answer.

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Q: What are all of the values of x ,such that Σ.. (-1)" + 1 converges? (31)"

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Q: converges to 0 Select one: O True O False

A: It is a series with increasing powers of π/3

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

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Q: If Ea, converges , then n=1a, diverges n=1 an n=1 Select one: O True O False

A: given sequence are, given that 1st sequence is converges and we have to find 2nd sequence is…

Q: etermine and justify if ∞ In(x) k=2 (1+k) ³/2 converges or diverges.

A: given series ∑k=2∞ln(x)(1+k)3/2

Q: Determine whether the following converges or diverges. 2n + 1

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Q: E (1- nsin-) converges n = 1

A: Series convergence test problem.....

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

A: We have to use GP sum Common Ratio.

Q: F) nー1

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Q: . Use the inegral test to show that =1 converges. 1+n2

A: To solve this question first we check derivative of function is negative for n&gt;0 and then we show…

Q: show : ΣΣ - a"d, (x - a)" | n=0 m=0 is convergent,

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Q: The sequence {x}=0, where xn 20" is convergent.

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Q: The sequence {x}=0, where xn (A) True (B) False 20 = is convergent. n!

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Q: If > an converges, then a converges. n=1 n=1

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

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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: 2n+1 4. Use the definition to prove that ) converges.

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Q: Find the interval of convergence for Σ 5 k?xk+1 ek+1

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Q: Show that n* 3-" converges for all exponents k. n=1

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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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