2. Using the Integral Test, determine whether the following series converge. k 00 a) E =1x2+1 1 b) ER=3v2k-s Σ=3 1 c) Σ=ok2+4

Q: Find all the values of x such that the given series would converge. (-1)"8¹xn (√n + 2) The series is…

A: 1. Given series is ∑n=1∞-1n8nxnn + 2 By Ratio test we get limn→∞8n+1xn+1n+1+2×n + 2xn8n < 1⇒ x…

Q: Find the interval of a-values for which the following power series converge: (b) Σ (ar-1)" 17" n=0…

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Q: 2 – n I-2 n3 +1 n=1 3

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Q: 2k 3. Given: Verify that Integral Test applies and use it to conclude whether this series is (1+;x),…

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Q: 3k3 +1 k6 – 4k3 + 2 k=1

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 5n 6n + 3 n…

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Q: the bot test to determine it the use tollowing series converges or diverges

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Q: .2 .4 x + + 1 2! +... 3!

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Q: 32. Show if the series converges or diverges using the Alternating Series test 00 1n+1 Vn n=1

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Q: 5. Expand the function into a power series (a) Show that X 1- x - x² Σ n=1 fnxn f₁ = f2 = 1, fn+2 =…

A: In this given question We know that  1) If power series converges for |x-a|<R Then Radius of…

Q: For the power series Σn=1 (–3)” n find its interval of convergence. √n

A: The given problem is to find the interval of convergence for the given power series. Given power…

Q: Determine if the following scries converges/diverges: n+ 166 12 – 165 =13

A: We are asked to find the series is convergent or divegent