l x such that the

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A: We have to solve given problem:

Q: k 75. k k=1

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Q: For which positive integers k is the following series convergent? Σ (n!)2 (kn)! n = 1

A: We have to find the value of K so that given series converges.

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A: Explanation of the answer is as follows

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A: The given series is: ∑k=1∞ 2·2-3k3-2k 4k+1

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A: We can re-write the terms in the series as

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A: Since you have asked multiple questions, as per policy, only first question is answered.

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A: Let's find.

Q: If f is a function such that f(0) = −3 and f ' (x) = 2f(x) for every value of x, find the Maclaurin…

A: f0=-3  &  f'x=2 fx Consider, f'x=2 fx Differentiating with respect to x, we get f''x=2 f'x Again…

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A:

Q: Determine whether the following series are convergent or divergent. +o0 (-1)* k2 – 2 k=4 +o0 1 b.Σ…

A: Part (a): ∑k=4∞ -1kk2-2 Apply alternating series test: The series has an=-1nbn or -1n+1bn where bn≥0…

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A: We are given the series,                                 . Note that,

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A: ∑k=0∞78k+2

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A: This is a problem related to series and sum calculator. Please follow the procedure given below.

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A:

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A: So by cauchy root test it is absolutely convergent.

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Q: Determine whether the following series converge.

A: Determine whether the following series converge.

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Q: Determine whether the following series converge. Justify your answers.

A: Consider the given series ∑k=1∞1k2+1k5

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A: Here the given series is  a∑n=1∞-1nnn+1b∑n=1∞1n-11·3···2n-12n-1!

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Q: determine whether the series converges absolutely, conditionally, or not at all.

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Q: Find the first four nonzero terms in the Maclaurin series for the function. f(x) = In (1+x)

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Q: Determine whether the following series converge. Justify your answers.

A: Given: ∑k=1∞kkk+2k

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A: Given: ∑k=1∞ k4ek5 To determine: Whether the given series is convergent or not.

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A: