Expand into a power series with center zero and determine the interval of 2 – 3x3 convergence. Write your answer in summation notation.

Q: 2. flx= -1

A: 1+xn = 1+nx +n(n-1)2!x2 +n(n-1)(n-2)3!x3 + ...

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A: You have posted multiple questions. As per norm, we are soling only the first question. If you need…

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A: Given series is   1+13+15+17+19+ . . . . . . . . hence seies can be written as ∑n=0∞12n+1

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A: To determine if the series is convergent or divergent series.

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A: Expressing terms as a telescoping sum:∑n=4∞ 8n2-14∑n=4∞ 2(n+1)(n-1)4∑n=4∞ 1n-1-1n+1∑n=4∞…

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A: Given∑n=2∞ne-n ...(1)e-n=1enNow substitute this value in equation (1) we get that∑n=2∞nenNow we…

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A: Given series,

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum.

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Q: Determine the series converges or diverges:

A: Series divergence test: If  limn→∞ un≠0 then the series ∑n=1∞un is divergent.   Now the given…

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Q: 2. Expand 1 into a power series with center zero and determine the interval of 2 – 3x3 -…

A: We have to find the power series and determine the interval of convergence.

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A: Given series is ∑n=1∞(-1)n3n24n2-1

Q: Determine whether the series converges; if so, find its sum. Otherwise type N in the blank. 1 Σ k(k…

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Q: k=1

A: The given series is: ∑k=1∞ekk3 Let, ak=ekk3, k>0 Now,

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A: solve the following

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A: According to question given ∑n=5∞2nn-4

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A: Given data: The given expression for the series is ∑n=0∞-17n. The expression for the series can be…

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A: This question is related to infinite series, we will solve it using given information.

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A: Telescoping series are series in which all but the first and last term cancel out.

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Q: tank

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Q: determine whether the series converges or diverges.

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Q: Determine whether the series is convergent or divergent. If it converges, find its sum. E , 3"+12-2n

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Q: Determine whether the series converges or diverges: 3"

A: Determine whether the series converges or diverse.