a, where a, = (-1)"+". n2 + 9 Consider the series n=1 Using the alternating series error estimation theorem, what is the smallest number of terms needed to estimate the entire sum with an error of magnitude less than 10-82 At least terms are needed.

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A: We will use ratio test to check convergence interval

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A: from x = - 1/2 , left end included (Yes) to x = 1/2 , right  end included (Yes)

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A: The given series is ∑n=1∞xn(6)n(n+6)

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A: The given series is: ∑n=1∞(2x)nn7...(1) Let, an=(2x)nn7; n≥1

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Q: n! 11) E 100 n%=D1 5n 72

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A: To use the n-th term test to test the given series.

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