6. 5. Let's consider the absolute series of terms of the absolute series: 7. Is LM8 n=1 (-1)-1 7+2n n=1 (-1)-1 Write down the first four 7+2n n=1 Is the (-1)-1 7+2n absolutely convergent? n=1 (-1)-1 7+2n conditionally convergent?

Q: 13. Verify that the alternating series test applies to the series S (-1)" (-1)" (n² + 2)10 Then use…

A: We need to first verify whether the alternating series test applies to the given series.…

Q: (п +2)(х — 3)" Find the values of z for which the series2(-1)". п(n + 1)5" converges.

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Q: 6. Are the following series convergent? Why? (a). (b) 00 n=1 α 2 (3n-1)1.3 n=1 n2 – 1 2η2 + η

A: The given series are ,  (a).        ∑n=1∞2(3n-1)1.3 (b).         ∑n=1∞ n2-12n2+n (.)  Necessary…

Q: `6. Evaluate the following geometric series as exact numbers. If the series diverges, then state…

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Q: ) Find the exact Sum of the following అఅయా 47.(and! series 25 A, 2. D-1

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Q: (4) Σ n=2 3n η3 x 5m (4)

A: Given series is then So we have Then from D'Alembert series test ,we conclude that given series is…

Q: (-1)"n(z- 4)" 3. Find the radius of convergence and interval of convergence for the power series 2n

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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: 3 (7) What is the value of the scries -? Justify your answer. (n + 1)2"||

A: Explanation of the answer is as follows

Q: 4.- Suppose we have a number with infinite decimals of the form 0.d₁d₂d3d4... (where each d₂ = 0, 2,…

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Q: 5.- Demonstrate that the series converges or diverges. n=1 3n+2

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Q: 5). Determine whether the series converges or diverges. ∞ n + ln(n) n2 + 17n − 12 n = 1 Which…

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