E. Suppose that the S, satisfies both lim,-o0 S20 = -1 and lim,-00 S2n+1 = -1. (That is, the sequence given by the even terms of Sn and that given by the odd terms of S, both converge to -1.) Show that also lim-oo Sn = -1.

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Q: Let x1 = 1 and xn+1 1 for n e N. Show that this sequence is convergent and find its In + 2 limit.

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Q: Prove that the sequence given by 2.4. 6.(2n) Un = 3.5.7.…(2n + 1) converges and find its limit.

A: Given query is to prove that sequence converges.

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A: We will use Triangle inequality.

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Q: Given that lim n2(x- 5)" converges by the Ratio test. If x€ Z then the numerical n- 00 value of x is…

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Q: Suppose an 20.If limn→∞ an+1 = L,then an 1. If 0≤ L 1,then 1 ak diverges.

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Q: Given that lim n²(x– 5)" converges by the Ratio test. If x € Z then the numerical n- 00 value of x…

A: This is a problem of power series.

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Q: because 01. > 1. 1. en n-00

A: If x>1 then limn→∞xn does not exists.

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Q: Determine whether the sequence converges or diverges. 4n7t an = tan 3 + 16n lim an = DNE - 00

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: converges for all * > 0 because lim a - In n 0, for all * > 0- n=2 True False

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Q: For the sequence {a_n}up ∞ down n=0 with limn→∞ a_n=0, this means the sequence diverges. T/F

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Q: Suppose xn2 0 for all n E N and the sequence (-1)"xn converges. What is its limit?

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Q: { { In(n) 5n² Sn=1 Determine whether the sequence converges or diverges. If it converges, compute…

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Q: Consider the recursively defined sequence s1 = 1 and sn+1 = 1 / (3-sn) for n  ≥1. i. Prove that sn…

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Q: The sequence (tanh n) converges to2

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Q: Suppose 1 aj = 2 3 4 5 aɔ = az = as = 1 1 3 4 4 5 6. 6. a) Find an explicit formula for a,: b)…

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Q: For the sequence {a„}, with lim a, does not exist, this means the sequence diverges. Select one:…

A: 1. Let {an}∞n=0={(-1)n}∞n=0 is an oscillating sequence and for this:an=-1; n is odd1; n is…

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Q: Use Theorem 4 from Section 10.1 to determine the limit of the sequence, or state that the sequence…

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