Determine if the series 2n=1(-1)"(1 – 2n)" converges (C) or diverges (D). Justify your conclusion for C or D by showing all your work and indicating all test names that you used and conditions for conclusions. NO justification, NO credit! (Test names : Geo, NT, IT(P — series test), DCT, LCT, ACT, AST, RT, NRT)
n 7) Determine if the series converges or diverges med n? - 2n-1 determine for what x-values it converges absolutely and for what x- (2x-11)" 8) For the power series n? values it converges conditionally
Determine whether the following series converge or diverge. Fully justify your answer. T(-1)"(n? – 2n) 400n3 + 78972 2
Does theta(n^3+2n+1) = theta(n^3) hold? Justify your answer.
Determine whether the sequence an = ln(2n + 1) - In(n +2) converges or diverges, and if it converges, find the limit. Find the length of the curve defined by x = 2t3, y = 3t2, osts 1.
Problem 2. Determine whether the sequence { "" } converges or diverges. Justify your answer.
Use the integral test to determine whether the series converges. Show all work to justify your answer. vands n=1 Select one: O A. diverges O B. converges
Question 2 (12 marks) (a) Consider the sequence with terms 2n3 5"5 log n , n = 1,2,3,.... an 13 n8n (i) Determine whether {an} converges or diverges. If the sequence converges, find its lmit (ii) Determine whether diverges. Justify your answer an COnverges or n-1 (b) Consider the series (2n)! 2" (n!)? n=1 and determine whether it converges or diverges. Justify your answer
Question 2 (12 marks) (a) Consider the sequence with terms 2n3 5"5 log n , n...
Do the following series converges or diverges. Justify your answer. (a) sin?(n) n2 n= i M8 M8 nh (b) 22n 221 n=1
2n Determine whether the series Σ is converges or diverges by the p-series Test. n=1 n4