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Suppose q is a constant and q> 4. 2"(n + 1)! (a) (5 marks) Does the...
o Consider the series an whose partial sums are denoted as Sn for n > 1. n= 1 (1) If an = m+2, does an converge or diverge? Explain. n = 1 (2) If Sn = 7+2, does [ an converge or diverge? Explain. 111
(a) (6 marks) Does the series (–19* sin( , ) converge or divergor Justi (a) (6 marks) Does the series converge or diverge? Justify your answer and state any test(s) you used. (-1)" cos(4n) (b) (2 marks) Consider the series . Explain why the Alternating Series Test can NOT be consider the senes 2 2n3 . used to determine whether the series converges or diverges.
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)?
Consider the set of all functions from {1, 2, ..., m} to {1, 2, ..., n}, where n > m. If a function is chosen from this set at random, what is the probability that it will be strictly increasing? (A) (n)/m”. (B) (%)/nm. () (min-1)/m". (D) (matema!)/n".
Consider the series (n=1 and infinite) ∑(−1)^(n+1) (x−3)^n / [(5^n)(n^p)], where p is a constant and p > 0. a) For p=3 and x=8, does the series converge absolutely, converge conditionally, or diverge? Explain your reasoning. b) For p=1 and x=8, does the series converge absolutely, converge conditionally, or diverge? Explain your reasoning. c) When x=−2, for what values of p does the series converge? Explain your reasoning. (d) When p=1 and x=3.1, the series converges to a value SS....
Does the series converge or dliverge? 1. nel n Does the series converge absolutely, converge conditio 2. n-2 vn-1 3nn! 3. Does the series converge or diverge? 2-6.10.(4n+ 2) Does the series converge or diverge? 4. 2 nln n Does the series converge or dliverge? 1. nel n Does the series converge absolutely, converge conditio 2. n-2 vn-1 3nn! 3. Does the series converge or diverge? 2-6.10.(4n+ 2) Does the series converge or diverge? 4. 2 nln n
1 2 3 n-9n2 1. Consider an = 1+ 2n - 5n2 (a) (3 points) Does the sequence {an} converge or diverge? Show your work. (b) (3 points) Does the series an converge or diverge? Why? 2. (8 points) Use a comparison test to state whether the given series converges or diverges. 3. (6 points) Does the given series converge or diverge? If it converges, what is its sum? § (cos(n) – cos(n + 1))
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
Assume that the sequence defined by a1 = 3 an+1 = 15-2·an is decreasing and an > O for all n. Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)