13. Verify that the alternating series test applies to the series S (-1)" (-1)" (n² + 2)10 Then use the one term error bound for an alternating series to find n=1 the least N such that the Nth partial sum, SN => (n² + 2)10 , approximates Swith error at most 1o-20. What are the first ten decimal digits of S? n-1

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A: Using for error bound:

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A: Let's find.

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: 11) Use the Ratio Test to determine whether the series converges or diverges. (-4)2n n2 n=1 IM:

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A: Solution of the problem as follows

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Q: 1. Show that each alternating series converges 2 b. Σ(-1)" 3n+1 n=1 a. Σ(−1) n=1 n+1 n+1 n n² +1

A: