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

Q: true or false: if the sequence [a sub(n)] is monotone decreasing, then [a sub(n)] must converge

A: Follow next step

Q: 8. Give the first five terms of the following recursively defined sequence: a1 = 2. and ar = ax-1 +…

A: Recursive definition of a sequence is one in which one term can be determined using previous terms…

Q: 6. Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence…

A: We have to examine the given sequence abouts its property

Q: 6. Does the sequence converge or diverge? If it converges, then find the limit. an- nª-3e" 2e" + nª

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Q: 21

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Q: Find the limit of the following sequences or determine that the sequence diverges: 1.

A:

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

A:

Q: The greatest lower bound for the sequence {0.1,0.01,0.001, 0.0001, ...} is

A:

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: 3. Determine if the sequence xn = 47² is convergent or not and find its limit if it exists n²+1

A: We want to find the given sequence is convergent or divergent.

Q: ((7) 2c-4 lim.

A: Given: limn→∞1+1nn As we know from the limit rule: If the limit limx→afxgx and its result of the…

Q: Does this mean the sequence is always convergent?

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

Q: 6. Find the limit of the sequence. You should consider the behaviour of the continuous version of…

A:

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: 7. Find a formula for a, of the sequence { 3, 6, 9, 12, ..}, assuming that the pattern of the first…

A: Given sequence is 3,6,9,12,..... Here, we have a2-a1=6-3=3a3-a2=9-6=3 So, a2-a1=a3-a2 Therefore,…

Q: 4. Let a₁ = 1 and an+1 = √8+ an Show that the sequence {an}1 is convergent and find its limit.

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Q: Determine if the sequence find its limit.) 1 { ( ₁ + 3 / 2 ) ² } 3n is convergent. (Hint: see if you…

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Q: 4. Find the limit of the sequence an = 2arctann n³ +4

A: The given sequence is

Q: Consider the sequence {10, -2, ) Find a formula for the general term an of the sequence, assuming…

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Q: 6. Consider the sequence defined recursively by 1 2 an+1 = an + N an If ao = 1, does the sequence…

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