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

Q: Show that the sequence {f}, where f₁²x) = tan `nx, x70 is uniformly ノ on any interval [a,b], aso but…

A: Given function as fnx=tan-1nx, x≥0

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

A: Use the defination of convergence of a series.

Q: 00 Σ n(Inn) n=2

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

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

A: The given series is

Q: 13. Determine if the Senes converges or birerges? 18 2n (inin)" n3 2

A:

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: 6. Use e 6 delinition and prove that he soquence, baving general term converges to 3.

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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 &lt; 1 then the series converges absolutely; if L &gt; 1 then the…

Q: (b) Use the comparison test to determine if the following improper converges: 5/T +1 7+x + x²

A: According to the given information it is required to check for the convergence: ∫1∞5x+17+x+x2dx

Q: If C.)" converges, then C,)" converges. n=0 n=0 Select one: True False

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Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

A: Explanation of the answer is as follows

Q: MEDI is a) converges to 2 b) converges to 2/2 c) converges to 23 d) diverges e) None of all

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Q: 7. Use the Ratio Test to show that has radius of convergence 3" R = /3. n=0

A: To find the radius of convergence: a) find the (n+1)th term which is denoted as an+1 b) find the…

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: Find Sn for the serks n= Does the seres converge ?

A: Consider the given series. Sn=∑n=1∞1n+3-1n+4 Expend the series and find the limit…

Q: 3. Use the Integral Test to show whether or not the converges. n(In n)19 n=2

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Q: 4. Does cosnx uniformly converge in [a,b] c (0, 7)? n =1 n

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Q: Σ Show that n2 + 1 converges/diverges n

A: The given series is: ∑n=1∞nn2+1 Let  an=nn2+1,n≥1    =nn21+1n2   =1n1+1n2 And, bn=1n

Q: ) Prove that if XnXnand YnYn are any two sequences of real numbers such that XnXn converges to xx…

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

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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: #2. Give a counter exa mple that (Sn) is bounded but not convergent.

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Q: If 0< by <1 for all k and , br converges, then , converges. Lk-1 %3D1 Select one: True O b. None of…

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Q: b. Eel/n – el/n+1 n=1

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Q: 34. Assume that an+1/an converges to p = 4. -1 Does > an converge (assume that n=1 An # 0 for all…

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Q: Vn +1- n –1 n=1

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Q: Find the smallest positive integer n so that S, approximates the sum of the convergent ser to four…

A: Here we have to find the smallest positive integer n so so the Sn, approximates the sum of the…

Q: + 4* 2) What does converge to?

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Q: Hiw.which ef thefellowing serier which conditiunally converge absolutely converge and

A: Find the sum of the series.

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: 7L The sequence Converges to 2e Converges to 1 Diverges Converges to 0 O REDMI NOTE 9 PRO P AI QUAD…

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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: Help please

A: Consider the given series:

Q: If a power series ∞ n=0 anxn converges absolutely at a pointx0, then it converges uniformly on the…

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Q: The integral S x3 converges to Select one: O True False

A:

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: 27 n! n=0 converges to 0. 8.

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

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Q: 8. Use the integral test to determine if IM8 k² (k³ + 2)3/2 converges.

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Q: By ratio test, n!7" O None of these O Converges O Diverges OiInconclusive

A: The ratio test: For the Power series

Q: If 21ak converges then E,ak, converges for any ak subsequence of ak.

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Q: 8. Suppose ar > 0 and Does > ak converge or k diverge? Why? %3D

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Q: Suppose > anconverges to 8 and > b,n converges to 5. What does (Зап — 2b) сonverge n=1 n=1 to? n=1…

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Q: (4) Suppose {a„}1 converges to L and that a, 2 0 for all n. Prove that {Van}1 converges to L. Tip:…

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Q: 1.4 Does (fa(r)} in 1.3 converges uniformly on |-3,3]? Explain.

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Q: 2" Зп+2 n=0

A: