cos(na)(2n2 +n-1) 1+n3 conditionally convergent, absolutely convergent, or divergent? Justify your answer. 00 ). Does nsin converge or diverge? Justify your answer.

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Q: n+1 Determine whether 2%3D1 n²/n converges or diverges. Give reasons for your answer. Paragraph B I…

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Q: (21) Determine if the sequence if convergent. Explain your conclusion. (a) Cn n²-1 n²+8 (b) Cn (c)…

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Q: The Cauchy condensation test The Cauchy condensation test says: Let {a,} be a nonincreasing sequence…

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Q: If an diverges and 0 (-1)"an converges. n=1 B)>(-1)"b, converges. n=1 c) 2(-1)"bn diverges. n=1 D b,…

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Q: An example of: Σ(an/bn) may diverge even though Σan and Σbn converge (show each step please)?

A: We have to show that Σ(an/bn) may diverge even though Σan and Σbn converge

Q: (-1)" ( b) Σ 2n Test: diverges converges n=0 Reason: (e) * (1+ 4)" Test: diverges converges n=1…

A: Alternating series test

Q: Let f(x) = e-0.5x on [0, 1]. Check the conditions of the fixed point theorem and subsequently…

A: To determine whether the sequence (p0,p1,p2,…) defined by the iterative process pn=g(pn−1), with…

Q: Let an > 0 and assume that an diverges. Write Sn = a1 + a2 + • ·.+ an. Prove the following…

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Q: For which values of p does Σ en n=1 (1+e⁹n) 8p PE converge? (Give your answer as an interval in the…

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Q: 23k-2 00 . Use the ratio test to determine if > 'k²3?k+1 converges or diverges. k=1

A: We have to find the given series is convergent or divergent by ratio test.

Q: a, > 0 and Ea, converges, then (-1)"an converges O False O True

A: This is Not True. Hence False is the correct answer. We will prove this by taking an example, Let…

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Q: Let f(x) = with po e 0.5 on [0, 1]. Check the conditions of the fixed point theorem and subsequently…

A: Given f(x)=e−0.5x on [0,1].Fixed point theorem:If g∈C[a,b] and a≤g(x)≤b for all x∈[a,b], then g has…

Q: Determine whether the following statement is true or false. If the statement is true, prove it, and,…

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Q: п? + 12 6) E Зп? + 4n — 1 n=1

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