2. Which of the following series diverge by the BDT? (Σ(-2) k=0 ê (c) Σ Σ(1+1)" Σ(6) 13 (e) none of these (d) n k

Q: Which one of the following p-series is divergent?

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Q: 6. Which one is the Maclaurin series of the function e³x² ? (b) (c) (d) (e) iM8 iM8 iM8 M8 M8 Σ n=0…

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Q: 8. Find the value of p for which the series 2n Inn (In (In n))" is convergent. n=3

A: the given series,        ∑n=3∞1n ln n.lnln n p

Q: Nhich of the following p-series are divergent? 00 ロと-4 S ロEsk-品 Σ 6666 10000 k38 ロと-7 1 k=7 ロEk…

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Q: .19. Evaluate the series: S(x) = Σakxk, k=0 where (a) ak = 1,

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Q: 1 (11) Σκ(F+2) k=1 (1.2) Σ k=1 4k (2k-1)(2k)(

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Q: 1 4. Use the power series for f(x) I arctan x to approximate the value arctan 11 the first four…

A: Given informationUse power series of

Q: The series obtained by differentiating term by term the series (x- 2), (x-2)', (x – 2)* | (x - 2) +…

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Q: For which (positive real) s does the series co nv er g

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Q: E1 (arctan(2n+1) – arctan(2n – 1)) n=1

A: The given series is: ∑n=1∞tan-1(2n+1)-tan-1(2n-1)

Q: Which of the followings are divergent series? 5+2" 1. 00 II. En=1 4n-1 I. E (sin1) IV. E cos…

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Q: 2.3 bech you have given the following: 2n + 1 (-1) n 4an+2 Czn +1)! (2n n= 0 find Ine Sum of this…

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Q: The series Eb, = 5" is divergent %3D n=19n +3 n=1 Select one: O True False

A: Let us use geometric series to determine whether the series is divergent or not in the next step.

Q: Q.2

A: The answer is given below.Explanation:

Q: 1 x" (а) п1 — х1 n=1 (-1)" (b) E x2 – n² n=1 8.

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Q: Which of the following is a power series about x 0? O Vx + v2x + V3x + v4x +... O 1 2 3. 4 +... x2…

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Q: Suppose f(z): N=0 5" 27 (z - 7)" e "f(z) dz to within 0.0001, it will be necessary to add the first…

A: Given that the function is                             fx=∑n=0∞5nn!x-7n To determine: ∫6.97fxdx…

Q: 2b. Find the range of value of x for which the following series is convergent or divergent 2'x? 22x3…

A: The given series is x1+21x22+22x33+23x44+... Here an=2n-1xnn We will check its convergence by…

Q: 19. Show that (for n = 0, 1, 2,..) (a) F(-n, b; c; 1) = (c-b)n (c)₁

A: We have to show F-n,b;c;1=c-bncn Solution: By Pochhammer definition cn=Γc+nΓ(c)           (1) and…

Q: 4. Determine whether the following series converges or not. n=1 1 2n+1+√3n-2

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Q: 72 (G) 3 n=1 1 (k) n(Inn)2 n=2 Inn Vn n=1

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Q: By inspection, which of the following series would Leibniz's Test for conver- gence be suitable and…

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Q: Match each Power Series with it's centre. One of the series is not a Power Series, so match that…

A: The power series with center "a" is given by: ∑n=0∞an(x-a)n

Q: 25. Which of the following alternating series diverges? (-1)*** (n – 1) (C). 5(-1)*! In (n + 1) (A)…

A: The answer is given by using convergence property of alternating series as follows :

Q: Q1: A- Find the limits of the following series (-1)" ܐ R=0 22 Στη Σ iv- 6 (2n-1X2n+)

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Q: Which of the following is a divergent geometric series?

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Q: 3x Which of the following is a power series representation of the function F(æ) = -? (6 – 5æ)(6 –…

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