# 3: (a) If the sequence or series converges find the limit. If not state DNC...
4. It's important to state definitions precisely Imprecise definition: A sequence an} converges to a limit a if, as the sequence continues, each term is closer to a than the previous term. (a) Find a sequence an} and a real number a so that lar+1- a every nE N, but an does not converge to a lan-a for _ Solution (b) The converse isn't true either, find a sequence {an} that converges to a real number a, for which the...
State whether the sequence {an} converges as n → 0; if it does, find the limit. (2n +4 " An = 3n+3)
Question 3 (18 points). Determine whether the given sequence converges or diverges. Find the limit of each sequence (including too if appropriate) or state that the limit does not exist (DNE). Prove all of your claims and reference the theorems on sequences that you are using. Hint: The fifth word of this question is sequence, not series! (a) an = (-1)" sinn
(b) Determine for which values of x the following series converges and find the limit for all the values of x where the series converges: (-1)" sin(ne) n n=1 Does this series converge uniformly on R? (c) Find the value of M8 1 n4 n=1
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
Determine if the sequence converges or diverges. If converge, find the limit. iii. an (1-2) ni!
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) a, = 5 + 8n2 " n + 8n2 lim n >00 an = Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) an = e-9/vñ lim n >00 an =
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) 1 1 1 1 1 2' 5' 3' 6' 4' 7' {*}**, 3,..} liman
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) 5n =tan 3 + 20n a. n
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) an = n^4/n^3 − 4n lim n→∞ an =_____