J Q2) Which of the following sequences and series is converge and which is diverge? (choose five): 10n 2) En=1n Ln=1 (n+1)42n+1 - n%3D1 ++1 1 3) En=1 4) an = vn(vn + 3 - yn) (2n+1)3 n 5) a, = " n 6) %3D n+1' 1+lnn

Q: 5k 3 k=1 k4+1 k%3D1 co

A: Follow the steps.

Q: Determine if the following series converge or diverge. Show all of your work. cos“(3k) k4 (a) k=2 4k…

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Q: E-1 cos(nn) e-n Zn=1

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Q: Determine whether or not the series of functions {Sn(x)} = {> xk-1} converges uniformly on [-a, a]…

A: We shall use the basic knowledge of power series and notions of converges and we shall use the…

Q: Determine whether or not the series converges

A:

Q: Find the interval of convergence of the series. (х- 4)7 Σ In (n + 9) n=1 О А. 3sx<5 О В. 3<x<5 O C.…

A: Given

Q: Consider the series 5 (2- 4)7 (z – 4)" 27 n + 4 n=0 Find the interval of convergence of this series?…

A:

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: 1 (а) 4n² – 8n + 3 n=1 In n (b) E(-1)". n2 n=2

A:

Q: (-1)" 2+ yn TL

A: The given series is ∑n=1∞-1n2+n. Solution: Let us denote the given series generally as , ∑n=1∞an So,…

Q: Determine the interval of convergence for the series E n=0 3.7.11.15. .. (4n+3)(2x+1)" 3^(n³ + 3n) O…

A: To determine the interval

Q: Determine whether the series converges. 2k – 1 k=1

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Q: 1 Prove that the series converges n(ln n)3 n=2

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Q: Find the interval of convergence of the series. (x – 1)" n42" n=0 O A. -3<x < 3 О В. Х<3 O C. Osxs2…

A: Ratio test

Q: 3. Use the integral test to show whether the series converges or diverges 00 п a) E- 00 1 b) E: n=4…

A: Integral test:  Suppose f(x) be a continuous, positive and decreasing function on the interval [m,…

Q: Let 2 c,x + n = 0 be a power series with the 7 radius convergence R Then the series diverges at…

A: Given series is: ∑n=0∞cn(x+12)n  and has radius of convergence R=72

Q: 3. Determine whether each of the following series is convergent or divergent using the appropriate…

A: To check the convergence of the given series.

Q: Q3: Find the interval of convergence of the following series Vnx" Σ Σ n-o Vn + 3" IM

A:

Q: Find the interval of convergence of the series. (x - 4)" Σ 5+ 2n n= 0 O A. 2sxs6 13 27 OB. O B. 5…

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Q: Determine whether the series converges or diverges. n2n Z (1 +n)3n n=1

A: As per the root test for the infinite series ∑n=1∞an if limn→∞an1n is less than 0 than the series…

Q: Σ (qk)! (k!)a k=0

A: Radious of convergence

Q: +oo 1 (2n)! ( a) Σ ( c) Σ-1)" 4n2 – 8n + 3 n=1 2" n=1 +00 In n (b) Σ-1)" n2 n=2

A:

Q: Determine whether the series L Tk+ 2)! 7 k! converges or diverges. a) cannot be determined b)…

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Q: n+2 9. Determine if the series converges or diverges using the Integral Test. n=1 n+1

A: To determine: The series is ∑n=1∞ n+2n+1 converges or diverges using the integral test. Concept…

Q: Find the radius of convergence for the series 3 n³ xn 3n OR=3 O O OR= 8 n=1 R = R= - الله R = 1 8

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Q: Find the center and the radius of convergence of the power series: * (4n)! 2" (n!)a (2 + ni)". n=0

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Q: e) 1 Σ Vn n=1 3 f) 5 3 п-1 п 8 W

A:

Q: Is the series convergent or divergent? Explain in minimum of two sentences. +00 n2 – 1 n2 +1 Un n=1…

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Q: 1. Determine the convergence or divergence of the following series Vn+1- yn Σ а. п

A: Here , To Determine the convergence or diverges of the following series,  we will use limit…

Q: The interval of convergence for the series 3n n= n=1 2" + n³ ( – 1)" is

A:

Q: ach of the following series converges absolutely, converges conditionally, 3n + 5n + 2 Vn8 + 2n² + 1…

A: We have to check for Nature of given series

Q: 8. Which of the series converge, and which diverge?: n+1 (2) Σ S 3 (c) 1 1 + ln²n (Inn)² n³ (d) n 1…

A: Disclaimer: Since you have posted multiple sub parts of question , we will solve first three sub…

Q: Consider the series: こ+u n(n + 1)2"+1 Express this series as a telescoping series: 0. n+ 2 n(n +…

A: Given that the series is              (n+2)/{n(n+1)2n+1}

Q: Find if the series converges or diverges from n=0 to n=infinity (k*ln(k))/((k+1)^3)

A: Given data is: ∑k=1∞klnkk+13  To find the series converges or diverges. [Note that the index cannot…

Q: Please use the Root test, Ratio test, and power series to solve these.

A:

Q: 1.2 Show that the series does not converge uniformly on R but the convergence n! n=0 is uniform on…

A: Given series is ∑n=0∞ xnn!. We have to show that this series does not converge uniformly on ℝ. First…

Q: Determine whether the series converges or diverges. n2n Z (1+ n)3n n=1

A: Explanation of the solution is given below...

Q: Find the radius of convergence of the power series Σ 6h z 4n n=0

A:

Q: Find the sum of the convergent series. 1 1 (a) 2n 3n n=0 (b) (sin 1)" n=1 9 27 +... 8 (c) 8+6+ + 2 1…

A: a) ∑n=0∞12n-13nb) ∑n=1∞sin 1nc) 8+6+92+278+...... Note:     Multiple parts are given, we are answer…

Q: 8 of 17 Rewriting 2nc,x"1+6cx1 as a ningle series whose general tem involves x", it becomes n=1…

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Q: Q3: Find the radius and interval of convergence of the following series (x+2)", (9 M) (n!)3 x" 2.…

A:

Q: Determine if the series converges or diverges.

A: Series: ∑n=1∞ 2nn!We need to apply ratio test:an=2nn!an+1=2n+1(n+1)!…

Q: Determine whether the series converges or diverges. 00 n + 1 Σ 4n2 + n + 1 n = 1 I O converges

A: We apply comparison test to check whether the given sum is converges or diverges In comparison test…

Q: Find the interval of convergence for the power series (-1)" Vn 5n (* – 3)". - n=1

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Q: 8) E )" (*)" n+ 5n-1 n+2 9) E 10) E +s Zn(n= 11) E Cos () 12) Σ. 5n 3n(2n+4) 13) Σ

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Q: Which of the three series (i) E (-1)n-1 cos2(n) (-1)n - 1 In(n) (11) E (-1)n -1 4 (iii) n= 1 n=1 7n…

A: (i) The given series is: ∑n=1∞(-1)n-1cos2nn3 Let, an=(-1)n-1cos2nn3;n≥1 Then an=(-1)n-1cos2nn3…

Q: 3n+1 (a) Zn=1 4" (b) E 1 1 In=1 Vn Vn+1

A: We solve (a) by D' Alembert ratio test and (b) by sequence of partial Sum

Q: Select ALL series which are convergent. 7 E1(-1)"n 5 Ln=1 (-11)n+1 En=0 62 n 92 n 7 En=1 O E sin ( )…

A:

Q: 3. Determine whether each of the following series is convergent or divergent using the appropriate…

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Q: Determine whether the series converges. 1 k=1 Vk + 11

A: This question is related to the series convergence or divergence.