o Consider the series an whose partial sums are denoted as Sn for n > 1....
Suppose q is a constant and q> 4. 2"(n + 1)! (a) (5 marks) Does the sequence {an}, where an = – -, converge or diverge? Justify your answer. 2(n+1)! (b) (6 marks) Does the series - converge or diverge? Justify your answer and state the name(s) of any test(s) you used.
Consider the series
a. List the nth term, Sn, of the sequence of partial
sums for this series.
b. What does the series converge to?
(3) Prove that the symmetric group Sn is nonabelian for all n > 3.
Find the interval of convergence of the power series: > (-2)»/n + 1(2x + 1)N+1 n=0
1 n+00 2 n=1 A sequence {$n} of partial sums of the series an has the property that lim Sn = Which of the following is true? 1 (a) lim an = 0. (b) lim an (c) lim an does not exist. (d) There is no way to determine the value of lim an. n+00 noo n+00 n+00 1 n The sequence {en} of partial sums of the series an has the property that sn = n=1 for every positive...
For the series <1-1n in n +1 n=1 1. Does it converge? 2. Does it absolutely converge? Please present your work in 1 pdf file with 2 pages (ONE subproblem per page)
2. (8 points) Let {fn}n>ı be a sequence of functions that are defined on R by fn(x):= e-nx. Does {{n}n>1 converge uniformly on [0, 1]? Does it converge uniformly on (a, 1) with 0 <a<1? Does it converge uniformly on (0, 1)?
DO NOT COPY OTHER ANSEWERS!!!!
2. (10 points) Let (%)n>o be a simple symmetric random walk. Compute P(Sn-y|S,n-x) for the two cases n > m and n < m
3. Let(Sn, n > 0} be a symmetric Random Walk on Z. Defined To-inf(n-1 : Sn-0) the time of first passage to state 0, prove that PlT, = 2nlSo = 0] = 2n.plsøn = 이So = 0] for any n 2 1
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?