Bonus. Suppose that {a,}n is a convergent sequence and that {b„}n is a divergent sequence. Can the sequence {an + bn}n converge? Explain your answer in detail.

Q: 5. What is meant by the index of a term of a sequence?

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Q: 4*++3" Consider the sequence a, = (a) Is the sequence monotonic pr non-monotonic? If it is…

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Q: What is the closed form for the infinite geometric sequence beginning  4,2,1,1/2 where the first…

A: Given :The infinite geometric sequence : 4, 2, 1, 12, ..

Q: Determine whether sequence having the given nth term is monotonic           an = 3 + (−1)n

A: an = 3 + (−1)n We need to determine whether the sequence having the nth term is monotonic or not.

Q: A town has a population of 5000 persons, but is expected to grow by 2% every year. 1. What would be…

A: Given A town has a population of 5000 persons, but is expected to grow by 2% every year. 1. What…

Q: (a) Give an example of a bounded monotonic sequence that converges to 2.

A: Note: As per bartleby instruction when more than one question is given only one has to be answered.…

Q: The sequence with general term an = (-1)" is divergent. True False

A: The given sequence is divergent.

Q: Determine whether the sequence defined as follows is convergent or divergent?   a1 = 1       an+1 =…

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Q: Give an example of a sequence satisfying the condition. (a) A monotonically increasing sequence that…

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Q: determine the limit of the sequence or show that the sequence diverges. an = √n + 5 − √n + 2

A: Determine the limit of the sequence or show that the sequence diverges. an = √n + 5 − √n + 2

Q: 3 if it exists. 8 Find the infinite sum of the geometric sequence with a = - 5, r = |

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Q: If $\$ 1000$ is invested at $6 \%$ interest, compounded annually, then after $n$ years the…

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Q: 2) Find the sum of the first 100 terms of the arithmetic sequence: 2, 4, 6, 8, 10, 12, ...

A: The arithmetic sequence: 2,4,6,8,10,12,.......

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A: Given : -1,-5,-9,-13,-17

Q: a,=(- 1)" is a divergent sequence

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Q: What is an example of a sequence that converges to 5?

A: A sequence is convergent to a point "P" , if there is a point "P" which repeats infinitely many…

Q: Does the sequence {n2 / 2n} converge or diverge?

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Q: What is the 8th term of the sequence whose ?th term is defined as ?? = (−1)^n(3n-2)

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Q: a1=1 , an+1=4-an , n is greater than or equal to 1 is the sequence convergent or divergent?  what if…

A: Given that a1=1 and an+1=4-an, n≥1 Write down the first few terms of the sequence: a1=1, Substitute…

Q: True or False For a geometric sequence with first term aj and common ratio r, where r + 0, r + 1,…

A: Let geometric sequence is a1,a1r,a1r2,a1r3...........a1rn-1 where a1 is the common difference and r=…

Q: This is a sequence, which test should I use and is it convergent/divergent? Explain. {(-1)n (n+1),…

A: This is a sequence which test should I use and is it convergent/Divergent? {(-1)n(n+1)!/3n!}…

Q: Does this mean the sequence is always convergent?

A: We can take limit of the sequence.  limn→∞an=limn→∞-1n-1nn+n

Q: Determine whether the sequence {(3" + 5")/"} is convergent or not.

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Q: determine the limit of the sequence or show that the sequence diverges.

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Q: Determine whether the sequence with  an = n*e-n for n = 1, 2, 3, . . . is increasing, decreasing,…

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Q: sequence

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Q: 1. Determine if the sequence converges or diverges and show how you arrived at the conclusion In n…

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Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: The given sequence is an = (3/2)n A sequence an is monotonic when its terms are non-decreasing…

Q: ´In (1/n)l

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Q: Find the infinite sum of the geometric sequence with a = 5, r = 4 if it exists. %3D 8

A: Given, a=5 r=4/7 S∞=?

Q: Find the infinite sum of the geometric sequence with a =2 r=2/6 if it exist

A: The geometric sequence with a =2, common ratio r=2/6

Q: 4 if it exists. 8. Find the infinite sum of the geometric sequence with a = 5, r = I.

A: The infinite sum of the geometric sequence with the first term ''a'' and common ratio r  is   .…

Q: how that the sequence (1 – (-1)" +1/n) is divergen

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Q: Determine the limit of the sequence or show that the sequence diverges. If it converges, find its…

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Q: 7. Provide an example of a monotonic decreasing sequence that converges to 1.

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Q: What is a divergent sequence? Give two examples.

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Q: Find the limit of the sequence defined by an n + 1 %3D 4"

A: The given sequence an=n+14n

Q: Find a formula for the n th term of the sequence an whose first five terms are 0, 2, 6, 12, 20?

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Q: Find the infinite sum of the geometric sequence with 3 if it exists. a = 2, r =

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Q: converges

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Q: n! Determine whether the sequence 1.3.5... (2n - is convergent. 1)

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Q: Find a convergent subsequence of the sequence {(-1)" (1 – 4)}, -

A: We need to find a convergent subsequence of {(-1)n(1-1n)}n=1∞.

Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: Given: an=4-1n

Q: {(1 -)'} 4 48.

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Q: The sequence convergent to Answer:

A: The solution is in step 2

Q: determine whether the sequence {√ n+2 - √ n+1} is convergent or divergent

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Q: Find the infinite sum of the geometric sequence with a = 6, r = if it exists. %3D %3D

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Q: How can you know if a sequence diverges or converges?

A: Answer :  We can know that a sequence is  diverges or converges ,  We have to remember that of a…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.