91. Show that if E-1 a, and En=1 b, both converge absolutely, then so do the following. a. (a, + b,) b. Σα. n=1 n=1 c. 2 ka, (k any number) n=1

Q: Which of the following statements is true? O E )" converges to - 2-1 7 12 O E O"' diverges n-1 O E…

A: The geometric series 1+ar+ar2+ar3+....…

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

A:

Q: 00 Σ n(Inn) n=2

A:

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: 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: I need To find a Sequence of functions (m c^(E-!, 13) That is cavchy Cuith Il ) and does not…

A: Given: C1-1, 1 To find: A sequence of functions in C1-1, 1 which is Cauchy but not convergent in…

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

A:

Q: 6. Use e 6 delinition and prove that he soquence, baving general term converges to 3.

A:

Q: Suppose ak > 0 and there exists M >0 so that E ak < M for all n E N. Prove that ak converges. k=n…

A: Suppose thatak&gt;0 and there exists M&gt;0 such that ∑k=0k=nak&lt;M , for all n∈ℕ. To prove that…

Q: Write the first five terms of p_j= j/(j+1) and then prove p_j converges to 1. Be sure to explicitly…

A: We have to solve an inequality for apsilon and j.

Q: Ean converges and an > 0 for all n , can anything be said about E? An

A: If ∑ an converges and an &gt; 0 for all n then ∑ 1an  converges         Proof :…

Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

A: Explanation of the answer is as follows

Q: Suppose that X₁, X2, ka)=P(X = _k) =1/2. Let Yn = Xn = n 2 Xi. are independent, such that, for each…

A: Chebyshev's Inequality Chebyshev's inequality guarantees that for a large class of probability…

Q: Suppose a,>0 for all n and 2 a, converges , which of the following must converge n = 1

A:

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

A:

Q: The following sequence : X(k) =( 1/k, e-k, (-2\k)+1)t is convergent to : Select one: a. X=(0, -2,…

A: Given , sequence is -Xk = 1k , e-k , -2k+1tLet ak =1kbk = e-k = 1ekCk = -2k+1

Q: Find Sn for the serks n= Does the seres converge ?

A: Consider the given series. Sn=∑n=1∞1n+3-1n+4 Expend the series and find the limit…

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

A:

Q: Let (c,) be a sequence converging to 3 with c,, 23 for all n. Which of the following conditions…

A: Option (a) is correct

Q: ht A: If S 2n – 2n²x x € [0, 1] fx,(æ) = { otherwise converges in distribution as n → 0. nt B: If 1…

A: Given that Xn : n≥1 is an infinite sequence of random variables and for each n, the density function…

Q: 4. Does cosnx uniformly converge in [a,b] c (0, 7)? n =1 n

A:

Q: so eskey ayン 1s Theorem : If En=1 an converges absolutely then it converges. 00 Н.W

A: Absolute converges means a series will converges even when you take the absolute value of each term.…

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: Answer the following True or False: Suppose that a,n 2 0 for all n and that > (an)² converges. Then…

A:

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

A:

Q: What number will A to converge to?

A:

Q: If Ea, converges , then n=1a, diverges n=1 an n=1 Select one: O True O False

A: given sequence are, given that 1st sequence is converges and we have to find 2nd sequence is…

Q: b. Eel/n – el/n+1 n=1

A:

Q: oll Show that sequence {n} n = 1, where .... 1/1₂ 0₂0₂...) converges 1/1,0,0 :) 9 9... 1/ng...) in…

A: We have to show that the sequence xnn≥1 defined by ; xn = 1, 12, ..., 1n, 0, 0,...  converges to  x…

Q: The seies Σο, + converges to 1 16 n=1 Select one: O True O False

A:

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: The sequence {(1 + 1)^² +1} 2n O O converges to e² is divergent ez converges to e 2 O converges to e

A: Sequence

Q: 25. Let an := n 2 1. Which of these conditions must be met if a, is to converge n+1 to 1? I. for any…

A: Just use definition of convergence.

Q: 00 00 Show that > n3 + 8n converges by using the Direct Comparison Test with En3. n=1 n=1

A:

Q: 5. If En-1 an converges, and if an +1 and a, > 0 for all n, (a) Show that E a converges. (b) Does E1…

A: Since, the sequence is a positive monotonically decreasing sequence, so, is also monotonically…

Q: 42. Given that la converges, does In (n) 1-1 (n²+5) ² $-10 converge or diverge? A. Dive B. Cannoe…

A:

Q: Answer the following True or False: Suppose that a,20 for all n and that, (a,)" converges. Then a,…

A:

Q: d (n, m): = 0 si n = m si n‡m 5-c(n-m)

A: Question seems wrong

Q: State which of the following is true. 1. If a sequence of functions (fn)n converges pointwisely to f…

A:

Q: Set an where r E R is a real number. Prove that ɑn converges to 0 if (-1, 1), cônverges tó 1 if r =…

A:

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

A:

Q: (e)M 00 4n+1. n=1

A:

Q: (a) Prove that 4280 k!pk k=0 converges for any r > 0.

A:

Q: B: To what value the following sequences can converge: Vn+3 %3D 1 4n+3 -Inn 2n2+1 1) an= 2) a,…

A:

Q: The sequence {C+1 In=2)"} N=1 converges to e² O None diverges converges to le converges to e³

A: The given sequence 3n+23n+1nn=1∞ The sequence can be written as follows:…

Q: 1 If ° 굶 dr 3D품. Then Σm1 00 +1 Select one: O a. converges to . b. converges but is not the sum of…

A: Answer and explanation is given below...

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

A:

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

A:

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

A: