1. Vn2+n-1 n=1 O converges diverges

Q: +0 Σ (2х — 1)" n V4n + 1 n=0

A: The given power series is ∑n=0∞2x-1n4n+1. Find the interval of convergence.

Q: Since lim k→+0 (k + 1)!/3k+1 k!/3* k+1 lim k→+∞ 3 +00, k! the series…

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Q: 3. Give an example of a convergent series Exn and a divergent series Eyn Ssuch that E(xn + yn) is…

A: Let ∑ xn be a convergent series and ∑ yn be a divergent series

Q: Find the sum of the convergent series.

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Q: The series Σ 6( − 1)*0.2-1.9/k○ diverges converges. k=0

A: We use ratio test to find the desired result.

Q: Find the interval of convergence of the power series S"(x-2)" n=1

A: We have to find the interval of convergence of the power series

Q: Vn 00 #1. E- n = 1 Vn° + 4n+3

A: As per our gudeline we supposed to answer only first question kindly repost other as next question…

Q: Indicate whether the series (-1)" n2 +1 n=1 Converges absolutely O Converges conditionally O…

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Q: (– 1)" is 4n1.17 + 3 The series n=0 O absolutely convergent O conditionally convergent O divergent

A: we have to test whether the given series is convergent or divergent

Q: Determine whether the series 1/1⋅2+1/2⋅3+1/3⋅4+1/4⋅5+…+1n(n+1)+… converges or diverges.

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Q: Find the sum of the convergent series. 6. Σ 9n2 + 3n - 2 n = 1

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Q: The following series Σ 3n-2" 5n+1 n=0 is convergent to

A: this is convergent series and

Q: In(k) k k = 1 O converges O diverges

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Q: ΣΗ In n n + 2 n = 1 O convergent O divergent

A: on using the limit comparison test  this series is divergent

Q: 2 Σ e -n=1 In +1)

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Q: b) The series sin(n°r) and 1+n³ n=1 n=1 are uniformly convergent on (0, 1).

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Q: 6. The series 00 is n+2n²+5 Divergent Convergent

A: In this question we will use basic of calculus i.e test of convergence of a infinite series. We wilk…

Q: is convergent Vn3 + 4n + 5 or divergent. n=1

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Q: (x+1)* (+x) 3k k=0

A: Find the radius of convergence

Q: Let pn = 5(6^n) + n^7/6^n. Show that, as n → ∞, {pn} converges to 5 linearly with rate 1/6.

A: Given that pn=5×6n+n76nTo showlimn→∞pn=5and rate of convergence=16

Q: n=1n2 +1 converges using 2 n =1 diverges using n =1 converges using 2 n =1 diverges using n =1 else…

A: Infinite series is the sum of the infinite sequence. A series is convergent if the sequence of…

Q: Since (k + 1)³/3k+1 ki3 /3* (1+ ±)* _ 1 lim k→+0 lim k→+∞ 3 3 the series…

A: The given series,       ∑k=1∞k33k

Q: Q3: Show that 3(2)n+2 3(2)n+2 is convergence and En=0 5n Zn=0 5n 20.

A: Please refer to the image below.

Q: The series k=1 5( − 1)k+1 - kl.1 O converges diverges.

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Q: 3n4 4n – 1 n=2 converges O diverges

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Q: Find the series' interval of convergence of (x* + * + })" x In(n) n2 n=3

A: Given series is ∑n=3∞x2+x+14nlnnn2.

Q: d) If Can's Converger and {b,'s diverges, Hhen fanton} Converges.

A: we argue by contradiction: suppose that an+bn converges. Since an converges by assumption, the…

Q: Since (k + 1)!/3k+1 lim k +1 lim k→+∞ 3 +00, %3D k→+0 k!/3k k! the series…

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Q: 1 3. Suppose f(x) = En-o x" .Assuming convergence, what is n=0 n! f'(x)?

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Q: 9. The series 3k+ (k+1)* is Convergent Divergent

A: We will solve the following.

Q: Vn + 5 Σ 3n2 + n + 1 n = 1 O converges O diverges

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

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Q: Find the interval of convergence of the series k(x+ 2)* 5k+1 k=1

A: The given series is: ∑k=1∞k(x+2)k5k+1...(1) Let, ak=k(x+2)k5k+1; k≥1

Q: 2. ∞ Σ Find the sum of the convergent series: n=1 1 4n2 –1

A: Find the sum of the convergent series 1/(4n2-1) from n= 1 to infinity.

Q: 8n 4n2 n = 1 + 1 f(x) = converges O diverges

A: Given query is to find integral converges or diverges.

Q: calculate the order of convergence for pn = (0.5)" and pn 0.52"

A: In this question, concept of convergence is applied. Convergence In mathematics, convergent…

Q: Since 3 (k + 1)³/3k+1 (1+ ±)* 1 lim k→+∞ lim k→+∞ 3 3 the series (converges/diverges/inconclusive)…

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Q: Find the sum of the convergent series. 1 n vn + 1. n=16

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Q: Does the series from 1 to infinity of ((-1)^(k+1))/((k+1)!) converge conditionally or converge…

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Q: 8. 1 The improper integral xp: V(x – 4)³ 4 Converges to -1 Converges to -4 Converges to 1 Diverges

A: To find the improper Integral  Take (x-4) = t And the limits accordingly Then integrate and put the…

Q: n! Determine whether E- converges or diverges. Zn=0

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Q: 1 i. Use the result in (i) to test for convergence 2n =1 2 Vn? +5

A: See the attachment

Q: Find the sum of the convergent series. 4 9n2 + 3n n = 1

A: Given: ∑n=1∞49n2+3n-2

Q: Find the sum of the convergent series. 2 9n2 + 3n – 2 - n = 1

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Q: Find the series' interval of convergence of (x² + x +) In(n) n2

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Q: The series (-1)"n²n! 2" n=1 O converges absolutely converges conditionally O diverges diverges…

A: Given series: ∑n=1∞-1nn2n!2nHere we have to check the correct option.