Consider the series Σ n=1 (2x)n n2 A) According to the Ratio Test, for what two values of x is the test inconclusive? B) Test the two values of x which were identified in Part(d) for convergence or divergence? Justify your answers.

Q: )c) Find the sum of each of the following series. (i) )ii) (iii) n = 2 8 n = 2 8 n = 1 n(n – 1)x",…

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Q: Use the alternating series remainder estimate to find what value of n required to estimate the…

A: First we shall state the ALTERNATING SERIES REMAINDER ESTIMATION result. If the alternating series…

Q: 1. Use the Alternating Series Test to determine whether the series Σ(-1)"+¹ converges absolutely,…

A: Alternating Series Test: A series ∑an where an=-1n+1bn where bn≥0, ∀n is convergent if (i)…

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: c. If the series has a sum, find the sum.

A: -12Explanation:If you have any questions let me know in comment box thankyou for your question.

Q: 3. Find the exact value of the series S = > n(n +2)* n=1

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Q: 3. Give an example of divergent series n=1dn and Ln=1 6n for which the series ("q + "p) converges.

A: Given: that An example of divergent series ∑n=1∞ an and ∑n=1∞ bn for which the series  ∑n=1∞ an+bn…

Q: Determine whether the series 3 (²) Σ 3(cos nm) n=0 n is convergent or divergent, and if convergent,…

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Q: 4. The series n=0 1-5m² n *** (a) is Absolutely Convergent (b) is Conditionally Convergent, but not…

A: Solution:-

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: State where the power series is centered Σ (-1)"(x – 4π) 9η - (9n)! n = 0

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