2) Prove convergence of In} using the Squeeze lemma: n2-3n+7 a) In = 73 - 4n...
convergence of 2:58-(3n-1) 3.7-11.(4n-1) o0 2.5.8 (3n-1) (x 1) Find the radius of convergence of A. B. 4/3 C. 3/4 I),2 D. O E. 3/2 O F. 1/2 О н. 2/3 convergence of 2:58-(3n-1) 3.7-11.(4n-1) o0 2.5.8 (3n-1) (x 1) Find the radius of convergence of A. B. 4/3 C. 3/4 I),2 D. O E. 3/2 O F. 1/2 О н. 2/3
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/
Using the limit comparison test, test the convergence of the series 3n+5 n2+10n+1
estimate error ∞ 4n (n + 7)3n n = 1
Prove the following: 1+4+7+...+(3n – 2) n(3n-1) 2
3n+3 3 (i.e. let &>0 and determine a n, to satisfy the definition of convergence.) Prove that lim n5n+5 5 Also, show, using algebraic evidence, that it is an increasing sequence.
Please note n's are superscripted. (a) Use mathematical induction to prove that 2n+1 + 3n+1 ≤ 2 · 4n for all integers n ≥ 3. (b) Let f(n) = 2n+1 + 3n+1 and g(n) = 4n. Using the inequality from part (a) prove that f(n) = O(g(n)). You need to give a rigorous proof derived directly from the definition of O-notation, without using any theorems from class. (First, give a complete statement of the definition. Next, show how f(n) =...
Find the interval of convergence for the series. (Enter your answer using interval notation.) 4n + 1 (-1)" +1 (5x) (2n + 1)! n = 0 (-00,00) Find the radius of convergence for the series. R = 4. [3/6 Points) DETAILS PREVIOUS ANSWERS Find the interval of convergence for the series. (Enter your answer using interval notation.) зах? n = 1 n 1 1 3'3 :) Find the radius of convergence for the series. R =
(-1)-1 n2 is absolutely convergent. 1. (2 points) Prove that cos n is convergent or divergent. 2. (2 points) Determine whether the series - (Use cos n<1 for all n) 3. (3 points) Test the series -1) 3 for absolute convergence. (Use the Ratio Test) 2n +3) 4. (3 points) Determine whether the series converges or diverges. 3n +2 n-1 (Use the Root Test) 5. (3 points) Find R and I of the series (z-3) 1 Find a power series...
Find the radius of convergence of 2"n!(x - 1)" n=02-6.10...(4n+2)