3.) Let ak E R with ak > 0 for all k E N. Suppose Σ㎞iak converges. Show that Σί1bk (By definition, for a sequence (ck), we say liCkoo if, for all M ER with Hint: Show that there exists (Ni))ไ1 with N > Nj for all j E N, such that bk there exists a sequence (bk)k of real numbers such that lim converges = oo and M >0, there exists N E N such that ck > M...
(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...
Determine whether the following series converges. 0 Σ 8(-1) 2k + 5 k=0 Let ak 20 represent the magnitude of the terms of the given series. Select the correct choice below and fill in the answer box(es) to complete your choice. A. The series converges because ak = of k>N for which ak+1 Sak: and for any index N, there are some values of k>N for which ak+1 ? ak and some values B. The series converges because ak =...
An n x n matrix is called nilpotent if Ak = 0 (the zero matrix) for some positive integer k. (a) Suppose A is a nilpotent nxn matrix. Prove that is an eigenvalue of A. (b) Must O be the only eigenvalue of A? Either prove or give a counterexample,
(4) Let A be an n × n matrix for which Ak = 0 for some k > n. Show that An = 0.
5. Consider the language L = {1'0/1k e {0,1}* |i >01) >0 Ak = i*j}; to show that Lis! not a regular language using pumping lemma, the correct choice for the word is: a. 10011 x=1- b. 1POP 1P Z=1 Le 1290? 12p* Z=1P OPS 2P Y-101 YEK d. 10P1P y=1" t:P
2)A 3 meter rod with a weight of 1000 N is suspended by two cables and has a large box(3500 N in weight ) tied to the right hand side hanging vertically. The center of mass of the rod is.5 min from the leftmost edge. One cable is exactly on the leftmost end of rod with a tension of 4000 N at an angle of 30 degrees to rod . The second cable is 1 m to the right of...
2. a. Define that the vectors α, α 2, ,Ak are linearly independent. b. Prove that α, α 2, ,Ak are linearly independent if α 0 and for every 0 < i k one has that α, κ α, > , αϊ-1 3. Find a linear system with real coefficients for which the span of
2. a. Define that the vectors α, α 2, ,Ak are linearly independent. b. Prove that α, α 2, ,Ak are linearly independent if α...
Project in matlab. I have the correct ak value but not the
correct ao value. My code is attached below also
2. Determine and plot the magnitude and phase spectrum of the Fourier series coefficients a, that is, plot ja, I as a function of discrete frequencies Jok and La, as a function of discrete frequencies fok 03 025 蓋0.2 0.15 0.1 o o5 ·10-8-6 4610 phase -2 -2 8- t= 0: .01:4; 9- to = 4; 10- fo =1/4;...
3) What is the name of the nucleic acid below 0 0 5 O-P-OCH2 N" "O OH OH A. Adenosine 5'-monophosphate B. Guanosine-5'-monophosphate C. Cytidine-5'-monophosphate D. Uridine-5'-monophosphate E. Thymidine-5'-monophosphate