Which of the following information is correct for the sequence 3 dx 1 dx 1 dx dx {an}n=1 | 5. 7. (a) The sequence {a,} diverges to + (b) The sequence an} diverges to -m (c) The sequence an} converges to 2 (d) The sequence an} converges to 1 (e) The sequence an} converges to 0

Q: sin N 8) Show that converges/diverges.

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Q: {1- The sequence is en (i) 0 (ii) 1 (iii) None of these

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Q: 3 3) The Sequence of real function f(x) = x²+³ converges over a interval [1,1], dotally from th…

A:

Q: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

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Q: Use the root test to determine whether convergent or divergent from k=1 and ♾ of (9k+2/16k+1)^-k/2

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Q: for sigma infinity n=1 3/2^n-1 find the sequence of partial sums

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Q: ^n for all n>=6

A:

Q: 8. (a) Give an example of a convergent sequence (s) of positive numbers such that lim (s/s) 1. (b)…

A: (Sn​)=(1+n1​) (tn​)=(n)Explanation:

Q: a_{n}=\frac{(-3)^{n}}{n !}

A: Tn = (-3)n / n! Tn+1 = (-3)n+1 / (n+1)! Tn+1 / Tn = (-3) / (n + 1)

Q: 1. Consider the sequence defined by a = (-1)' · 2ª for i 2 0. Compute: (a) (b) I, azi

A: ∑i=02a2i=∑i=02-12i22i            =∑i=024i            =40+4+42            =21

Q: B){(sin(x))/x

A:

Q: Determine if the sequences converge or diverge.  an = (ln n)/ln 2n   an = e^-n ln n   an = (3n…

A: • Sequence 1: Inconclusive • Sequence 2: Converges (e^-n dominates) • Sequence 3: Converges…

Q: Do the following scquences {a„} converge or diverge? Justify your answers. (a) an = 3 (b) an –…

A: "Since you have posted a question with multiple suparts, we will solve  three subparts (d), (e) and…

Q: Converges or cliverges 2:0 Inci

A: Let's Solve,

Q: Converges or diverges

A:

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: Use limit comparison test for sum of n=1 to ♾ of (3n^3+2)^(1/2)/(8n^2+9n+1)

A: take bn = 1/n  we know that if limn→∞anbn= finite  then by limit comparison test both series behave…

Q: Only use epsilon defination , Let be a sequence of positive terms such that pn-> p show that…

A: We apply only Epsilone defination.

Q: 1. Let a, = 1 and an+1 = 1+ 1+an (a) Find the first six terms of the sequence {an}. (b) Prove that…

A: As you asked multiple sub parts so I answered 1st three subpart.

Q: Which of the following information is correct for the sequence 7. 9. dx 1 dx 1 dx 1 dx {an}n=l 5 (a)…

A:

Q: 9.) Define what is the sequence {Xn} diverges n = ∞ as meant by to +00/-00

A: A sequence {xn} diverges to +∞ as n approaches infinity, it means that the terms of the sequence…

Q: use the formulas: i=   n(n+1)/2  and i^2=  n(n+1)(2n+1)/6  express the sum below as a function of n…

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Q: The series 2n +2 Diverges to-o0 Converges to 1- Converges to B Diverges to +

A: Given series is ∑n=1∞sinπ2n-sinπ2n+2 The Nth partial sum of given series is…

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.