true or false: The sequence {ak } and the series ? ak both converge?
3. Consider the sequence {ak} = 1 = 1. -1 1 -1 1 -1 2 5 6 Select co ܠܛ the true statement: A The sequence {ak} and the series Ļak both diverge. B. The sequence {ak} converges, but the series [ak diverges. c| The sequence {ak} diverges, but the series [ak converges. D| The sequence {ak} and the series ak both converge. E None of the above.
1. Here is a sequence of partial sums of the series ak: 5n+3 n+4 / k= 1 a) Give a 10. Show work below. b) Give ak, simplified. Show work below c) To what, if anything, does the series converge?
3. Consider the sequence {u}?, = {1,- - 1 1 - 1 2 '3' 4'5' 6 Select the true statement: A The sequence {ak} and the series as both diverge. B The sequence {ak} converges, but the series as diverges. c The sequence {ax} diverges, but the series ak converges. D The sequence {ak} and the series ak both converge. E None of the above.
help.PNGa. Find a formula for the general term . b. Does this sequence converge or diverge? Why? c. Does the series converge or diverge? Why?I did part (a) already since it was the easiest one and I got a_n=3/(4n). correct me if I am wrong. However, I do not know which test to use for part b and c.
Why is this one false? False A Fourier series will converge to the value of the function at all points if the function has a sentation convergent Fourier series repre- False A Fourier series will converge to the value of the function at all points if the function has a sentation convergent Fourier series repre-
mark true or false 8. If the seriesh converges absolutely then the series sin (kz) converges uniformly on R. 9. There exists a polynomial f such that its Taylor series centered at 1 does not converge to f. 10. If a sequence of functions (fr) converges uniformly on sets D and E, then it converges uniformly on the set DUE
(Exercise 4.13, reordered) Given a series ΣΧί ak, let 8,-Ση-i ak. Σχί ak is Cesaro summable if S1 + 82 +... +Sn lim n-+o converges. (a) Give an example of a series Σ00i ak that is Cesaro sum mable but not convergent (b) Prove that if 1 ak converges, then it is Cèsaro summable. Hint: Say the sequence of partial sums sn → L. Try to prove that =1 8k → L by showing and then splitting the latter sum...
(4) Let Σ ak and Σ bk be series with positive terms. The limit comparison test applies when a/bk L0; suppose for this problem that ak/bk0. (a) Show that if Σ bk converges, then Σ ak converges. Hint: remember we can delete finitely many terms from the series and not affect convergence. Use the fact a/bk0 to truncate the series at a convenient point. (b) Show that if ak diverges, then bk diverges. (c) Show by example that if Σ...
Series converge or diverge By using integral test, the convergence or divergence of following series can be determined.. * cos(n2 + 1 732 TRUE (because ...... FALSE Explain why. The following integral Converges by direct comparison test. TRUE because. .... FALSE because
n 12. Series A is om and series Bis Σ. A) both series converge absolutely B) both series diverse C) series A converges conditionally and series B diverges D) series A diverges and series B converges conditionally