8. Determine whether the series converge (a) k+5 Ση (b) k=1 1+2k+k² 1+ 3k + k²

Q: 3. Show that the series In 2+ (-1)k-1 -(x – 2)* k2k k=1 from Example 3 diverges when x = 0 and…

A: The given series is ∑an = ln 2 + ∑k=1∞(-1)k-1k. 2kx-2k.Putting x = 0, the series reduces to ∑an = ln…

Q: We want to use the Alternating Series Test to determine if the series: k³ √k7 + 10 k=4 (−1)k+2_…

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Q: Determine p and the radius of convergence of the sum Σ (n!)³²n² -x²n 2n (2n)! n=0

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Q: 2. Use the ratio test to determine the interval of convergence of the power series (−2)"+¹ (x−4)" 00…

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Q: 7. Determine whether the series Σn=1 n 5n 6n+2 is convergent or divergent.

A: Necessary condition for convergence  :                         Necessary condition for…

Q: Show that the series (a > 0, ß > 0) a +1 (α+1) (2x + 1) (B+1) (2ß+1) + 1+ B+1 + (a + 1) (2x + 1) (3a…

A: We will use ratio test for convergence    To  check a series ∑anit is convergent or divergent first…

Q: n² Determine whether the series En 3n+1 ln(n+1) 2n=1 is convergent or divergent.

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Q: Consider the series (k!)³ (3k)! k=0 Determine if the series converges or diverges.

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Q: (-1)*1 n +1 5) For the series n=1 a) Show the series converges by the alternating series test. b)…

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Q: compute the series  ∞Σn=1 1/(n2+2n)

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Q: verify that the series diverges

A: Step 1: Step 2: Step 3: Step 4:

Q: 1. ii) and ii): 4 Determine whether each series converges or diverges. Justify your answer for both…

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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: Σ n² – 3n + 2 n=3

A: Explanation of the answer is as follows

Q: | + 4 23 | s 97, 15 1

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Q: n³+2n²+3n-5 Does the series Σ=1 n6+3 converge or diverge? By what test?

A: `

Q: Determine the convergence or divergence of the series 70 + 1 gn Σ n = 0

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Q: (a) Give an instance of the Binomial Series which begins as follows: 10 1 - 6z² +24z¹ - 80z6 +240z8…

A: Given binomial series Note: According to the guidelines we are allowed to solve one question at a…

Q: Verify that the series converges

A: Step 1: Step 2: Step 3: Step 4:

Q: Determine whether the series 2-√√n +∞o Σ √√n n=1 converges or diverges using the Integral Test.

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Q: Use the Ratio Test to determine if each series converges or diverges (п — 1)! Σ 1 - (n +1)2

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Q: Compute 2" - 3n+2 5n-1 by explaining clearly why the series converges, and then actually providing…

A: A geometric series is convergent if its common ratio r<1. If it is convergent then it converges…