Use the knowledge that the limit of the nth term of the sequence of partial sums can be used to determine the behaviour of a series to determine whether the following sequence converges or not.

Q: Ex. Show the seguence whose nth term is In (n*) an %3D converges. 5n

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Q: Prove or Disprove: Every oscillating sequence diverges.

A: To investigate the convergence (or divergence) of an oscillating sequence.

Q: A decreasing sequence where cn is greater than or equal to 1 for all n. If this sequence could…

A: A decreasing sequence where cn is greater than or equal to 1 for all n. That is, cn≥1, the sequence…

Q: Show that the sequence defined by  a sub 1= 1  and  a sub n + 1 = 3 - (1/ a sub n) is increasing and…

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Q: Show that any sequence of positive real numbers either has a subsequence that converges, or else a…

A: We have to show that any sequence of positive real numbers either has a subsequence that converges,…

Q: a1 =-1, an+1= An +6 An +2

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Q: Determine if the sequence converges or diverges and show how you arrived at the conclusion In n² {a}…

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Q: consider the following infinite sum 1/2+1/4+1/8+ 1/16 + 1/32 +...   (b) Add up this sequence.…

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Q: Find the first four terms and the nth term of the sequence of partial sums associated with the…

A: 1, 2, 3, 4, ......, n, ....... Now first partial sum is, S1=1 Second partial sum is, S2=1+2=3 Third…

Q: If (an) is a sequence converging to L, prove that (an)=1 converges to L.

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Q: Find the sum of Partial Sums of a Geomatric Sequence 1+3+9+. . . +2187

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Q: 8. Determine whether the sequence a n3n converges or diverges.

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Q: 11. Explain why all the terms of a divergent geometric seriesare nonzero.

A: Solution: We have given geometric series: First of all, we are going to understand the concept of a…

Q: 2 a. Prove that if a, is a convergent series of nonnegative terms, then a, converges. 2 b. If we…

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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: (b) Decide the convergence or divergence of the sequence a = √8 and an+1 √8+ an.

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Q: A sequence that does not have any convergent subsequence

A: We find a sequence that does not have any convergent subsequence.

Q: Let an = n 2 1 In(2" + 1) Determine if the sequence {an}n=1 is convergent or divergent 00

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Q: Use the Monotonic Sequence Theorem to show that the sequence n 3n is convergent.

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Q: List the first 5 terms of the following sequence and determine whether or not it 4n2-4 converges: an…

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Q: For each of the following infinite series, determine whether the series con- verges or diverges. You…

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