3. If [an is a senies of poritive term amd Ian is convesgent ithen cheek the convergenie of the Sen'ts E an

Q: Show by an example that Panbn may diverge even if Pan and Pbn both converge.

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Q: Which of the following mfinite senes are convergent? Select all that apply. 100 100+50+25+... 1-D0 2…

A: Which of the following infinite series are convergent

Q: Suppose that a, > 0 and b, > 0 for n > N (N an integer). If lim, 00 1,¬- (an/bn) = ∞ and Sa,…

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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: 10. If * a, > 0 and an converges, then (-1)"a, diverges True False

A: Can we test the given statement as follows

Q: Show by example that E(a,/b,) may diverge even though Ea, and Eb, converge and no b, equals 0.

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

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Q: 13. Determine if the Senes converges or birerges? 18 2n (inin)" n3 2

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Q: . If [an is a senies of pobitive terms md [an is convergent then cheek the convergenie of the…

A: Comparison test : If 0≤yn≤xn for n≥k for some k .Then  If ∑n≥1xn is convergent then ∑n≥1yn is also…

Q: If Ian is a senies of paritive terms omd Ian is convegent then cheek the convergenie of the Sen'rs I…

A: Let ∑an is positive integer and ∑an is convergent then we have to prove that ∑an1 + an is…

Q: Suppose an 20.If limn→∞ an+1 = L,then an 1. If 0≤ L 1,then 1 ak diverges.

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Q: 7N 8N 3) Show that converges/diverges.

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Q: 5. Use the Limit Comparison Test to show that E=1 1+k2 1 100 Lk%31 converges.

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Q: is it seies converge ost not. 1-2)^

A: To find:

Q: Show that if an < o0, then E In(1+an) converges if and only if an converges. n=1 n=1 n=1 Hint: show…

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Q: If o an is convergente then o nan is divergente Select one: O True O False

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Q: Suppose that xo 22 and xn = 2 + √xn-1-2 for ne N. Use the Monotone Convergence Theorem to show that…

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Q: (b) Give an example to show that the product (fngn) may not converge uniformly.

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Q: the valu e of P. for ubich for allna). fntegral Converges

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Q: ii. Investigate convergence or divergence of 2n + 100 3n +1). n=2

A: Given series is  ∑n=2∞-1n2n+1003n+1n

Q: Shoe wheen vio dalar laror Converges oliveraes

A: Series convergnt and divergent

Q: If 2 a, converges, then la,| diverges. n=1 n=1 True False

A: Given statement is FALSE. I HAVE given a counter -example.

Q: 1 3. En=1 (2n+1)3

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Q: H.w. which of the fellewing serier absolutely converge and which eonditionally convere.

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Q: ) Prove that if XnXnand YnYn are any two sequences of real numbers such that XnXn converges to xx…

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Q: If an < bn and if En=1 an converges, then 1 bn also converges. True False

A: we can solve it by using comparison test.

Q: What number will A to converge to?

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Q: 2 an IS AB5OLU TELY CONVE RGENT! unbuznuo7 si juniz Convergent 7 E E\anl is divcrgent but Ean is…

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Q: 2. Prove that (1,1,1,...) converge to 1 in (R,).

A: Convergence of the sequence

Q: If E Un is absolutely convergent then (un)² is also n=1 n=1 convergent.

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Q: Hiw.which ef thefellowing serier which conditiunally converge absolutely converge and

A: Find the sum of the series.

Q: is it kue thak if Can) and Cbu) tuo sequences of real numbers such Hhat iaus bu for aull -nEN Iand…

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Q: 3. Discuss the convergence or divergence of E=1(2"e"). 4. If (an) is a bounded decreasing sequence…

A: As per guideline we have to solve one question

Q: 26) find the mternel of convergenu of tue power Senies (x-6)*-1 и -) 6 onsurs : aj (6,l2) d) (-6,6)…

A: A detailed solution is given below.

Q: If > an converges, then a converges. n=1 n=1

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Q: Q. By c/2silon definition , check the convergenie of fallowing sequenies the =

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Q: (-1)h 7^ (n!)? 2? (an+3)! A)is diverget B)is absolutely convergent O is conditionally conveglat

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Q: Show by example that E(a,/b,) may converge to something other than A /B even when A = equals 0. Σαν…

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Q: Dis cuss the Conditions For which Foun'er sevies is conv convergent ·

A: The objective is to show the conditions.

Q: true or false , prove your answer Suppose the interval (3, 3.99999) contains infinitely many terms…

A: Theorem:If a sequence is monotonic increasing in an interval then it's converge to it's supremum.

Q: the convergence or diver 3k Ek=1 k! 4k Zk=1 k2 - k

A: As per guidelines we have to solve only one

Q: Show that 2"x" converges if |x| <. n=1

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

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Q: 2End 2 povel seies expressan for the funchon flx) =dan'(sn) Whal o As interval or convergencl

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Q: The set S on wc fn Cx) = 1+ x" Converges pointwire ?

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Q: Does E 8. k=1 In(ek41) converge or diverge?

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Q: O Discuss the convergence of f,(x)=x + , on A =[0,00).

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Q: 8A Defermine whather the following sevier com fi fimnlly ow timnrge. s converges or そ (-1)"- an+7

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Q: (4) Suppose {a„}1 converges to L and that a, 2 0 for all n. Prove that {Van}1 converges to L. Tip:…

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Q: Is the Sertes ko convergend orcirergent Convergond.ordhrergent =1

A: