Decide whether or not the given sequence converges to a limit. If it does not, find, in each case, at least one convergent subsequence. We suppose n= 1, 2, 3,... xn = ∑ nj=1 ( 1/ j! )

Q: Evaluate Σ n=1 2 2 n' +4n+3

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Q: Determine whether the given sequence converges or diverges. If it converges, calculate its limit. an…

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Q: Determine if the sequence converges or diverges. If the sequence converges, find its limit: en + 1…

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Q: Find the limit of the following convergent sequences. 3+5n? a. an n+n? 2nn b. an = tan 1+8n

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Q: Mark each statement True or False. Justify each answer. (a) If (sn) and (t„) are convergent…

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Q: Determine whether the sequence converges or diverges. If it converges, find its limit:

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Q: If E Un is absolutely convergent then (un)² is also n=1 n=1 convergent.

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Q: Consider the sum S=>(2). Express S in the form where a, b e R and b #0, if it converges. If you need…

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Q: (c) (d) In n (−1)” +00 n=1 2n³ 3 n + +1 +00 n=1 n

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