Which of these series converges? Α.Σ2 k=1 ∞ k Β.Σ 20K-3 1 C. √√k k=1 3 Dak√k Ο.Σ.

Q: (sin z)2; 20 = 0 20

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Q: ΣΠ n=1 a. 1+4+1 6n 61 5 b. 41 5 is equal to c. The series diverges. d. 66 5

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Q: Calculate S3, S4, and S5 and then find the sum S = using the identity 4n2 – 1 n=1 4n2 – 1 2 2n – 1…

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Q: 12a) n=l 3+1 22n-3 12b) M=1 1 'n' + 9n + 20

A: Part a) ∑n=1∞3n+122n-3By using series ratio test i.e. an ≠ 0 and L = limn→∞an+1anL =…

Q: 5 cos n Determine the limit of the sequence a, %3D 1 6 4 Divergent 2 O O O

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Q: 2. fow く2 <a 30 20 Prove thot 大2 %3D n 21

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Q: 5 ΣΕ j=1

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Q: n-2 S. The nth partial sum of the series Ln =1an is given by Find the 8th term using the sum. n+3.

A: Option C  Is true 1/22.

Q: Find out whether the series given below converges or diverges. 00 Σ 5n + 8 n = 1 Choose the correct…

A: Comparison Test: Let us consider two series ∑n=1∞un,∑n=1∞vn such that un≤vn ∀n∈N Then ∑n=1∞un…

Q: Which of the following correctly expresses the series (3 +7+ 11 + 15 + 19) in sigma notation? a. Σ…

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Q: Find the smallest number n of terms needed to obtain an approximation of the series k=1 accurate to…

A: We have to find the smallest number n of terms needed to obtain an approximation of the series.

Q: lim オ→-00 や?-1 t.

A: Consider the limit  limt→−∞t2+2t3+t2−1

Q: G:- The G-M of positive values is 4. by including the fourth value becomes &.what is the funth value…

A: We know, geometric mean (GM) of n values a1 ,a2 ,...,an is given by, GM = (a1 a2 ... an)1/n Let, x1,…

Q: is a constant. . If |r| < 1, the sum of the geometric series E ark-1 is k=1

A: Known fact: ∑k=0∞ a rk=a1-r       provided r&lt;1.

Q: QA7. Considering the expansion of (V2+", n>= 4, if the ratio of the 5th term from the beginning to…

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Q: Q5// A. Draw a graph with the degree sequence 1, 1, 6, 4, 4. B. Consider the function b(n) = 4n+3…

A: This is a multiple part question . The solution to the given questions are explained below.

Q: For which values of p does E converge? n=1 (n°+7)*5 (Use symbolic notation and fractions where…

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Q: Find a power series solution of y" + (1+x²)y=0 13 5 + a. ao(1-x². √x6+)+ a₁(x-²x³- -x² +) - 24 720…

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Q: 23. If Y - 2xy = 1, y = 0 when z = 0, the first 2 dz non-zero terms in the series solution for y are…

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Q: Which of the following is the harmonic series? (A (B C D 20 n=1 1-2 n=1 n=1 n 2n n E n=1 (-1) n+1 n

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Q: What is the sum of the series below if c = 4.5, d = 11.7, and x = 0.3. 26) n=0

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Q: 22 22 –1 20 = 1

A: Consider fz=z2z2−1 and z0=1 We have to determine the Laurent series and residue about the given…

Q: HW4) 9.

A: Detailed explanation:Original FunctionFunction:    f(x)=(3+2x)4  Step 1: Zeroth DerivativeZeroth…

Q: Sn = Find a formula for Sn, n ≥ 1 for the sequence -2, 1, 6, 13, 22...

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Q: The series e² = 1 + x + + 2! 3! converges to e for all x. a. Find a series for (e). b. Find a series…

A: Given, ex=1+x+x22!+x33!+x44!+x55!+⋯ converges to ex for all x.

Q: Show that the following sequence of does not obey WLLN. p{*x 1/2 1 P{x, = + (2k – 1)"}= 2 %3D |

A: Answer: For the given data,