6. Check the convergence of the following series: (a) Σ (1+; )" 8 tan-¹n (b) 1+ n² 1/n (0) Σ Inn√In²n-1

Q: Determine the interval of convergence of the series 00 Ž (9x- 2)" n=1 n NOTE: Answer must be in…

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Q: 2. I) Find the centre, radius, and interval of convergence for the given power series. 1 Σ (13) n…

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Q: 6. Check the convergence of the following series: 8 n (a) (1+-!-)" 2

A: As per the company guidelines we are allow to solve one question at a time so i am solving first one…

Q: (a) For which numbers x does the geometric series E(3x – 2)" converge? (b) To what does the above…

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Q: nº (b) Test the convergence of the series L 8 by ratio test.

A: an+1an = (n+1)58n+1n58n an+1an= (1+1n)58limn→∞(1+1n)58 → (1+1∞)58 = 18

Q: sider the following series. (Enter your answers using interval notation.) Σ 7-1) n A-1 (a) For what…

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Q: (a) Tell about the convergence (conditionally/absolutely) of alternative series, which for an=1/n…

A: (a)   Alternative series ,for which an=1n                          ∑n=1∞(-1)nan≡ ∑n=1∞(-1)nn…

Q: In each part, obtain the Maclaurin series for the function by making an appropriate substitution in…

A: As per guidelines, we are supposed to solve only first three subdivisions. Please repost other…

Q: (b) Test the convergence of the series by ratio test. 00

A: Ratio rest is as follows

Q: (4-x)". /n 00 n+5 9n : 7" n=1

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Q: Test the convergence of the following series: (a) n=1 n+2" n²2" (b) 00 COS (nπ) n

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Q: Consider the series (-1)" (6x+5)" n=0 (a) Find the series' radius and interval of convergence. (b)…

A: We have to find- series radius and interval of convergence, values of x for which series converge…

Q: Suppose f: [a, b] → R is Riemann integrable. Let e > 0 be given. Then show that there exists a…

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Q: E(-1)" cos (1/n²) COS

A: Alternating Series: An infinite series of the form ∑-1n-1un whose terms are alternatively positive…

Q: Find an easy expression for the sum of the series on its interval of convergence. (-1)"-'n -x" 2"…

A: Given series is ∑n=1∞-1n-1n2nxn

Q: Σ'an where an n=1 = (−1)n+5 ( n² n? + 6 n? +5,

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Q: Consider the following series 00 1 (1) (2) ) (3) (-1)"n In n n(ln n)³ (n + 7) In(n + 7) n=2 n=2 n=2…

A: Given:

Q: 5. Use geometric series to show that: 1 (a) Σo(-1) k = 1 if−1 < x < 1 1 (b) Σ(x-3) = ¹ if 2 < x < 4.…

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Q: 01: Find the interval of convergence of the following series. 1. E(-1)"( ) 2. Ex 3. E(-1)" nx"

A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: Determine whether the series is divergent or convergent, and if convergent, then absolutely or…

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