1 2. Show that E 00 converges to X-1

Q: Ex 11.1.3 Determine whether {Vn 47 n converges or diverges. If it converges compute the limit.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: dæ x-1 1

A: Solution: The objective is to find whether the given integral converges or not

Q: 1 E(-1)"+1, ( n + 1 ) . 3η n=1

A: To find whether converges or diverges

Q: 3.5.13. Given n = N, let pn(t) = t" for t = [0, 1]. Prove that the sequence {Pn}neN converges…

A: Sequence and collection is one of the simple subjects in Arithmetic. An itemized series of factors…

Q: 1 is not convergent. Theorem 1.8.2 E n = 1

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Q: (x + n)² Show that h„(x) converges poimtwise to f(x) = 1, V x e [1, 00). %3| x² + n²

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Q: 00 a is converges, then lim a = 00. n=1

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Q: In(k) k k = 1 O converges O diverges

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Q: Suppose that an(x – 6)" converges for x = 10. At which of the points (a)-(d) must it also converge?…

A: Given: The given series is ∑an(x-6)n  The series converges at x=10. According to theorem is the…

Q: Find all values of x for which ) (3x)" converges. n=D1

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Q: 00 a) E (÷)" п X а) 4 n=0

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Q: Define effective interest rates and prove that r = i -1. 1+ n

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Q: b) Suppose (xn) does not converge to 0. Then there exists e > 0 such that all except for finitely…

A: Let us suppose the following sequence xn=1,0,1,0,1,0,..... We have to see that the odd terms are 1…

Q: 13.D. Show that, if we define fn on R by fa (x) 1+ n?x? then (fn) converges on R.

A: givenfn(x)=nx1+n2x2dividing numerator and denominator by x2fn(x)=nxx21+n2x2x2

Q: 6+ cos (7x) Perform a test to determine if x converges. T/ 7 00 5 dx X II

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Q: Find the interval of convergence of E 27" (x – 7)3n+2 n=0

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Q: Q3) The sequence a, = 1 - (0.2)" a) converges to 0 b) diverges c) converges to e d) converges to 1

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Q: 2. Let {sn}=1 be an unbounded sequence of negative numbers. Show {sn}n=1 has a 00 00 subsequence…

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Q: e-n n(n + 1) E(-1)"+1. n=l

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Q: E (1- nsin-) converges n = 1

A: Series convergence test problem.....

Q: 11. Suppose f and g are continuous positive functions. Provide an example such that diverges and…

A: We need to provide example for convergence.

Q: 1 Determine by the direct comparison test if Ln=1 2n+1 converges or diverges .

A: The given series is ∑n=1∞12n+1 We have to test the convergence

Q: (In(n))" 00 Find the value(s) of a such that 2 is convergent T2 Answer:

A: Given that, ∑n=2∞lnnan By using the integral test, ∫2∞lnnandn It can be written as, ∫2∞1nlnnadn

Q: If E an converges, then an/n12 converges. n=1 n=1 O True False

A: True, using Abel's test.

Q: For which values of p does En=1 00 en (1+e9n)4p converge?

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Q: 1 3) For which a does converge? Justify your answer. n(In n)e n=2

A: This question is related to series.

Q: 4. Which comparison would show that dx converges? x + e*

A: According to the given information, it is required to tell which comparison would show that the…

Q: 1 Use appropriate tests to determine if E(-1)"+1, converges. n* log(n) + n! n=1

A: use appropriate test to determine whether the series ∑n=1∞-1n+11n4logn+n! converges according to…

Q: If both E Un and E(-un) converges then E Un| n=1 n=1 n=1 is also convergent.

A: It is given that ∑n=1∞un and ∑n=1∞-un converges.

Q: ax Examine the convergence of , where a>1. x (log xy" +1

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Q: B) > n! (4x – 6)" is convergent for x = n=1

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Q: 2. For p>1, is S dx convergent? Inx xP

A: To show that whether the given integral is convergent for p>1.

Q: For which values of p does E=1 (1+eon)4p converge?

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Q: Match each of the following with the correct statement. C stands for Convergent, D stands for…

A: To answer the given questions we shall use the following tests  Comparison test: Let ∑un and  ∑vn be…

Q: 5. E-1 ne-" n=D1

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Q: Q3) The sequence a, = 1 - (0.2)" a) converges to o b) diverges c) converges to e d) converges to 1

A: Given an=1-0.2n

Q: If |Xn+2 − Xn+1| < |¤n+1 − xn| for all n E N then (xn) converges. -

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Q: Show that (- 2-1)* log k converges. k2 k=1

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Q: dx heorem 1.7.1 is convergent if and only if µ < 1. (x – a)H a

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Q: 5) Find all values of x for which En=1 nxn (n+1)(2x+1)n converges absolutely.

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Q: Question 14 State whether the sequence an = e -n/3 converges and, if it does, find the limit. а)…

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

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Q: 2) To what number does E-L T Converges? (-3)" m=1 gn+T

A: Given expression is ∑n=1∞-3n5n+1. Let the given series be ∑n=1∞un . ⇒un =-3n5n+1…

Q: 6) If an converges, then n=1 a) E converges. n=1 b) lim an = 0. n00 00 c) E(an)² converges. n=1 d) E…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: if 0, dx converges to 1 then c= се O a. -3 O b. 3 O c. 1 O d. -1 3 1/3

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Q: +00 1 dx xln*(ex) 4 e

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Q: Determine if the given is convergent or divergent. E0, In" (n*) 23n2 n=1

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Q: 3n Problem 1. Determine whether E test(s) you use. z=1 n² -6 converges or diverges. Clearly state…

A: see 2nd step.

Q: 1 3) For which a does converge? Justify your answer. n(ln n)a n=2

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Q: 8. of is g integerl the following For which values Convergent? dx

A: We need to find the values of a, b&gt;0 is the following integral convergent.…