For ln(1+1/x), determine if the sequence is bounded and whether it is eventually monotone, increasing, or decreasing. How can you tell?

Q: Show that the sequence {cn} = {(−1)n 1/ n! } converges, and find its limit

A: The nth term of the given sequence is .

Q: ter n minutes, the temperature of a cup of coffee, in degrees Celsius, is T 55 + 25e0.1n %3D e0.1n

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Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

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Q: Let x1 = 1 and xn+1 1 for n e N. Show that this sequence is convergent and find its In + 2 limit.

A: I have shown the sequence is bounded above and monotone increasing which implies sequence is…

Q: Find the limit of the following sequences or determine that the sequence diverges. {(ln (1/n))/(n)f

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Q: Find the sum, if it converges. 7i-1 ΣΤ 10 The sum is (Type an integer or a simplified fraction.)

A: Given,             ∑i=1∞ 7710i-1

Q: (E) The sequence defined by a, =1, a=-a, converges to 1.

A: Sequence is convergent if limit is finite.

Q: Consider the sequence (2n/n+1) n∈N  Find an upper bound and the limit of this sequence, if they…

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Q: Determine whether the sequence is convergent or divergent. If it is convergent, find the limit. an…

A: Given, an = ln(n +1) - ln n.

Q: Use all three methods, (difference, quotient, and derivative) to determine if the following sequence…

A: We can use addition or subtraction method To check whether  following sequence is increasing or…

Q: (b) Find the limit L of the sequence an = n° e° n+13 + n > 1 as n tends to infinity.

A: Topic:- limit calculus

Q: Use series to evaluate the limits

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Q: Find the limit of the following sequence or determine that the sequence diverges. {(n sin3…

A: Given:  Calculations: Calculate the following limit

Q: Find x so that x, x + 2, and x + 3 are consecutive terms of ageometric sequence.

A: We have to find the value of x such that x, x+2, and x+3 are consecutive terms of a geometric…

Q: Determine whether the sequence converges or diverges. 4n7t an = tan 3 + 16n lim an = DNE - 00

A: A sequence is called convergent if there is a real number that is the limit of the sequence. ... A…

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

A: For given sequence we have to check its convergence first we have to check    limn -> ♾ | (-1)n…

Q: Find the limit of the following sequence or determine that the sequence diverges. an = (e-n)/(2 sin…

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Q: ? 2 - n + 5n3 ? lim -6n³ – 3n + 4 lim ?

A: To find the limit, just I have taken common the highest degree term from numerator and denominator…

Q: explicit

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Q: Determine the interval and radius of convergence for E-1) (+1)*

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Q: The formula for the amount A in a savings account compounded n times per year for t years at an…

A: Since n represents the number of compounding per year that will be the variable that approaches…

Q: Use differentiation to determine whether the sequence is strictly increasing or 2n +1 Sn=1 strictly…

A: We will check sequence is strictly increasing Or decreasing by using derivative.

Q: Evaluate the limit of the sequence or state that it does not exist. an = ((1)/(n))1/ln n

A: Given sequence, an=1n1ln(n)

Q: 14. What does it mean that a sequence {xn} tends to infinity?

A: What can we say if the sequence tends to infinity .

Q: Find the limit of the sequence whose terms are given by 5 (n²) (1 – cos an

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Q: 15. Let a and b be constants with 0 < a < b. Does the sequence {(d" + b")/"} converge? If it does…

A: Given :             The sequence is an + bn1n      Definition of convergent :                  The…

Q: Find the limit of the following sequence or determine that the sequence diverges. {(tan-1 n)/(n)}

A: Given: The sequence, tan-1nn

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

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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: divergent For the following sequence, decide if it is convergent or sin ( + 4) 1 An

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Q: DA. The sequence {(- 0.002)"} converges by oscillation to the limit |

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Q: The sequence {x}=0, where xn 20" is convergent.

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Q: sin n An

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Q: Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each…

A: an=ln2n+1n Now, limn→∞an=limn→∞ln2n+1n=limn→∞12n+1·21       By using L'Hospital's…

Q: lim n-78 √√3n+2 3ntz 1 h

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Q: For any n N, define the function Xn RR by : if x ≥n Xn(2)= 0, if a <n. Show that the sequence of…

A: We will use definition of limit of sequence of function.

Q: Find the limit of the following sequence or determine that the sequence diverges. {(sin 6n)/(5n)}

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Q: Find the limit of the following sequence or determine that the sequence diverges. {ln (n3 + 1) - ln…

A: an=lnn3+1-ln3n3+10n

Q: The sequence (c} diverges.

A: To check whether the sequence diverges

Q: Give an example of a sequence of continuous functions: fn : [0, 1] → R that has no pointwise…

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Q: n17 + sin(19n + 7) n19 +7 Determine whether the sequence an converges or diverges. If it converges,…

A: Given the sequence is an = n17+sin19n+7n19+7

Q: For the following determineif the sequence is increasing,decreasing, not monotonic, bounded below,…

A: Given:  an =e3nn=0∞ To identify the sequence:…

Q: 30レて

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Q: 2n – 7 Prove that the sequence with nth u, = (a) is monotonic increasing, (b) is bounded above, (c)…

A: Given a sequence un = 2n-73n+2 a) It is monotonically increasing if  un≤un+1 ∀n∈ℕ We need to show…

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.