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: Decide whether the following series converges or diverges. (a) L n00 5n-2021n² , 7" 4"

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Q: Decide whether each of the following statements is true or false. If a statement is true, 8 8…

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Q: Consider the following geometric series. 00 - 1 (-8)" 9" n = 1 Find the common ratio. Irl = |8/9…

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Q: 18) Discuss the convergence/divergence of the following series: 2+(-1)" n=1

A: If we add the the terms of the sequence, we get an infinite series. An infinite series may also…

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

A: Ratio rest is as follows

Q: 12. Test each series for convergence or divergence. State the test used. (a) i Inn 8n n=1 (b) (-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)…

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Q: 4. Discuss the convergen (a) 2"e-n.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Part IV: Determine whether the following series are convergent or divergent. Use the nth term test…

A: The main objective is to check the convergence or divergence of the series.

Q: Item 2 Find the interval of convergence for the following series: (х — 2)" n² · 3n n=1 ANS:–1 < x <…

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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: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

A: The given series is ∑n=1∞-1n+1x-7nn7n. We find the interval of converges by using the ratio test.

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: Σ (-1)"+1 n³+1 n=0

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Q: 4. Determine whether each series is convergent or divergent. State clearly which test you use,…

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A: Given the function fx=ln2x-3.  We will use the Taylor series to calculate the series.…

Q: Which of the followings are convergent series? I. 5+2" Ln=1_2®i2 II. 0 Ln=1 _4n²-1 II. (sin1)" n=1…

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Q: Use the equation 1 1- x = ∞ n=0 x" for x < 1 to expand the function 6 1- x4 in a power series with…

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

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Q: 4) Determine the radius of convergence of the power series given by (5x – 3)" n5"

A: power series ∑n=1∞5x-3nn5n To find the radius of convergent of the  given power series

Q: TRUE or FALSE: 1. 8,128 is a perfect number. 2. There are integral solutions of the equation 30x +…

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