If £a, converges and Eb, diverges, can anything be said about their term-by-term sum E(a, + b„)? Give reasons for your answer.

Q: If 2n=1a, converges, and if a„ # 1 and a,n > 0 for all n, a. Show that E=1a, converges. b. Does…

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Q: By 6/2silon definition, check the Convergenre of the following Sequenies. = 2n21

A: Given that, Sn=2n2+12n2-1 We find the limit of this sequence as follows:…

Q: How would I find if the sequences an=nπ cos(nπ) and an= (n2)(1/n) are convergent/divergent?

A: To examine the given sequence regarding convergence, that is study the limits as n tends to infinity

Q: The sequence {( an+2 )"}1 n=1 O diverges converges to Je3 converges to e None converges to Je?

A: the given sequence converges to

Q: If gan converges and Σbn diverges, can anything be said about their term-by-term sum Σ(an + bn)?…

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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: 8. Determine by the ratio test if 2n=1 (2n)! converges or diverges.

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Q: n+1 (-3)*1 3n n=1

A: Ratio test : Suppose we have a series ∑n=1∞ an then define  c=limn→∞ an+1an . If 0≤c<1 then the…

Q: 20. Show that if E-1a, converges, then 1 + sin(a,) Σ n=1 converges.

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Q: If lim bn pe 0= =1 || En=1 a, converges, then En=1 b, diverges.? True False

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Q: {()} Find the rate of convergence of the sequence sin as n=1 n 0 . n n 3 n4 1 n-

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Q: N! 9) Show that converges/diverges

A: Use D Alembert ratio test

Q: 27 81 2) 16 – 12 + 9 – + 4 16 243 + 64 - - -

A: Given the series: 16-12+9-274+8116-24364+............ To check if the given series is convergent or…

Q: The sequence (n+(-1)" n Diverges Converges to 0 Converges to 1 Converges to e Converges to 2e

A: Option 3 is correct.

Q: State why the following intergral is improper and find the value if it is convergent: 2r (z² – 4) "

A: The given integral is I=∫262xx2-423dx The integral is improper as the integrand is unbounded at x=2.

Q: Are the following convergent or divergent? Show your work and state the reason 100 11) Ση n=0

A: The summation of n, n from 0 to 100.

Q: Indicate if the following statement is TRUE or FALSE. Briefly justify your response with an…

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Q: If a, converges and a, > 0 for every n, show that 4converges. What can you say about a for any…

A: Given: ∑n=1∞an converges and an>0 To prove: ∑n=1∞an2 converges. Proof: ∑n=1∞an2=∑n=1∞an2 Since…

Q: Which converge and diverge?

A: In this question, we have given four multivariable functions. for each of them, we have to check the…

Q: Suppose that anx" converges for x = 5. Must it also converge for x = 4? What about x = -3?

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Q: 8. 4+n2

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Q: The sequence Converges to e Diverges Converges to 0 Converges to 2e Converges to 1

A: First I have written the definition ofconvergent and divergent sequence and then that given sequence…

Q: If the infinite sum 7 k=2 k2 converges, use the Remainder Estimate to find lower and upper estimates…

A: Given ∑K=2∞1K72

Q: 00 k6 k! k=1

A: We have to apply the ratio test to the following series -  ∑k=1∞k6k!

Q: If 0< by <1 for all k and , br converges, then , converges. Lk-1 %3D1 Select one: True O b. None of…

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Q: 2 n 1 o Show that + converges/diverges n-

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Q: Is the series Σ (3j)"n! n" n=1 convergent or divergent? Give a reason for your answer and show the…

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Q: What number will A to converge to?

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Q: S sin(n) cos(n)/n converges or 3. Use to sandwich/squeeze theorem to argue whether the sequence 1+n…

A: We need to find if series converges or diverges.

Q: The sequence a, = sin (A) is unbounded (C) converges to a number less than 1 (E) diverges to…

A: Limit of a sequence

Q: Show that the series n' (2n)! is convergent. Deduce that lim (2n)! n=1

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Q: Vn +1- n –1 n=1

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Q: What are all of the values of x, such that converges?

A: We have to use GP sum Common Ratio.

Q: RIO

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Q: Find the smallest positive integer n so that S, approximates the sum of the convergent ser to four…

A: Here we have to find the smallest positive integer n so so the Sn, approximates the sum of the…

Q: The sequence Converges to e Diverges Converges to 2e Converges to 1 Converges to 0

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Q: en

A: We need to find the convergent or divergence of given series

Q: show : ΣΣ - a"d, (x - a)" | n=0 m=0 is convergent,

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

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Q: The sequence {x}=0, where xn (A) True (B) False 20 = is convergent. n!

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Q: The series 3 k 1 3. is 3. convergent to O None divergent convergent to 3 convergent to

A: We have to solve

Q: If \( \{a_n\}\)  is decreasing and bounded below then it is convergent.  true or false?

A: Monotone Convergence Theorem : Every bounded monotone sequence is convergent.

Q: If Ea,x" converges on the interval [- 10,10], where does the series a, (2x - 2)" converge?

A: The Series converges on [-4,6].

Q: If Ea, is a convergent series of positive terms, prove that Esin (a„) converges.

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Q: Determine if the sequence converges or diverges. If it converges, state the limit. an nsin = in 1.²1…

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Q: 8. Suppose ar > 0 and Does > ak converge or k diverge? Why? %3D

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Q: Suppose > anconverges to 8 and > b,n converges to 5. What does (Зап — 2b) сonverge n=1 n=1 to? n=1…

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Q: 2" Зп+2 n=0

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Q: If the sequence (xn) convergence to x, then the sequence (VXn ) also convergence .x to إختر واحدا:…

A: If the sequence (xn) is convergent to x then the sequence sqrt(xn) is convergent to sqrt(x). Thus,…

Q: Show that the series n" (2n)! is convergent. Deduce that lim 0. (2n)! n=1

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