1. Provide a complete and accurate e-N proof that the following sequences converge. That is, prov...
1. Provide a complete and accurate e- N proof that the following sequences converge. That is, prove these sequences converge. n2+2 (b) an- 30s n-cos(n) 3n+2 e) an-4m2-7 (d) {
Provide a complete and accurate e-N proof that the following sequences converge. That is, prove these sequences converge. 2Ti3 1 Provide a complete and accurate e-N proof that the following sequences converge. That is, prove these sequences converge. 2Ti3 1
Provide an ? N proof to prove that the following sequences converge. Question (e), please. 5. Provide an e – N proof to prove that the following sequences converge. (a) {ne cos(n)} (b) {zo Bom} (c) {(-1)In (n)} (d) an = 2 + 1 (@) an = V1 -
Prove that the following sequences diverge to infinity or negative infinity (c) { - e^n } (a) 120-1)) 3 n2 Hint : Provide an M - N proof that an approaches infinity (a) 120-1)) 3 n2 Hint : Provide an M - N proof that an approaches infinity
2 Determine whether the following the following sequences converge or diverge. If it converges, find the limit. (a) an = cos () 2n (b) a = In 2n + 1 3 (a) Does Î- (-)" converge or diverge? If it converges, find its sum. n=1 (b) Show how > 41-13-" can be written in the form of a geometric series. Does it converge or diverge? If it converges, find its sum. n=1
(6) (6 pts ) Determine if the following sequences converge or diverge; if a sequence is found to converge find its limit. Justify your answers in each case. 2 +3" b) 6" a) {tan"(n?)} n=1 nounce where
3. Determine if the following sequences converge or diverge. Show work. (1){1/27 +(3/87")"} (b) {(2/3)* + 1")"}
Determine whether the following sequences converge, and find the limit of those that converge a) (1+i)n b) 1/n[(1+i)n)] c) 1/n![(1+i)n)] d) 1/(1+i)n e) n/(1+i)n f) n!/(1+i)n
y, July AM 1. What does it mean for a sequence {a} to converge to a € R? State the definition (-1)+1 What about sequences that don't converge? Read the following proof by contradiction, and then complete Practice Question 6. Claim: {(-1)"} does not converge to any real number a. Proof: Assume that the sequence converges; that is, assume that there is an a E R such that lim,-(-1)" = a. Then, using & = 1, from the definition of...
Problem #10: Which of the following sequences converge? (i) an (-1)n+1 n n2 - 7 (-1)" n2 n? - (iii) an = cos(NT) (iv) an= sin(nn) (ii) an= -9 (A) (i) only (B) (ii) only (C) (i) and (iv) only (D) (i) and (iii) only (E) (ii) and (iii) only (F) (ii) and (iv) only (G) all of them (H) none of them