2. Prove from first principles (that is, give a proof following the form given in the original definition of convergence of a sequence) that the following sequences converge. (Hint: your first job is to figure out, informally, what the limit is in each case.) an Cn - = n+1 n+2' n odd 400/n -1/(400m²) n even { 400 I bn dn - - 5n 4n²-3' {n/(1+²) 15259000 n>

Q: 7. Let {an1 and {bn}1 be convergent sequences with limit A and 0, respectively. If bn 0 for all n N…

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Q: Write out the first five terms of the sequence with, [(1)"] determine whether the sequence…

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Q: (-1)^(n+1)/(sqrt(n)((lnn)^(2)). Prove that those are convergent but not absolutely conve

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Q: 8. (a) Give an example of a convergent sequence (s) of positive numbers such that lim (s/s) 1. (b)…

A: (Sn​)=(1+n1​) (tn​)=(n)Explanation:

Q: Write out the first five terms of the sequence with, [(1-8)] determine whether the sequence…

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Q: 2. If a 1 and an+1 = 3(1+) for each n> 1. 3+0 Does the sequence converge? What is the limit?

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Q: 7. Let {a,} be the sequence defined by a, = n cos(n7) n+1 Do the following. (a) State the theorem…

A: Answer

Q: Write out the first five terms of the sequence with, [(1 - 7)", determine whether the sequence…

A: To write out the first five terms of the sequence with 1-7n+7nn=1∞, to determine whether the…

Q: x = -1/n when n is odd, and an = 1/2" when n is even

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Q: 1. Determine whether the following sequence converges or diverges. If the sequence converges, find…

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Q: 1. Prove that the sequence {4+} converges to 4.

A: To know weather two function converge or not take difference of them and put limit to infinite. If…

Q: 4. For a sequence {n}, we define the arithmetic mean sequence {n} as X1 + X2+...+Xn n We will see…

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Q: Find the limit of the sequence if it converges; otherwise indicate divergence. an = 7 + (0.9)", for…

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Q: (b) Why? ) Consider the sequence {an = (-1)"}n€Z+· Is it divergent or convergent?

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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: ' Write out the first five terms of the sequence with, [(+)"] determine whether the sequence…

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Q: aпалyses). 3" a. an %3D 2n+2

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: (e) an (f) an = √n+1-√n (g) an = √n²+1 n = 2n n! [Hint: First prove that an ≤ 4/n for all n € N.]

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