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
Determine whether the following sequences converge, and find the limit of those that converge a) (1+i)n...
3. (18 pts) Determine if the following sequences converge or diverge. For those that converge, determine the limit of the sequence. Make sure to fully justify your answer! arctan(n) (a) an= n In +3 (b) bn = (-1)" n² + 40 + 4)
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
Q. 6 Determine whether the following sequences converge or diverge, and state whether they are monotonic or whether they oscillate. Give the limit when the sequence converges. {0.2"} a) {(-2.5)"} b) Q. 7 Find the limit of the following sequences or state that they diverge. sinn 27 2 tan in] n3 +4 b)
1. For each of the following sequences, determine whether it converges. If so, find the limit. 2n+1 5n-2 a. b. 4. =(-1)"." 2n 2"-1 c. n
6. ... / 6 points) Determine if the following sequences converge or diverge. If they converge, give the limit. (a) an = (-1)" n+1 n (b) an = n In(n)
number 4 1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series cos(x) (2n)! (-« <...
(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
2. Use the limit comparison test to determine whether the following series converge or diverge. n Α.Σ 2 + n3 n=2 2n3 - n B. S 3n5 + 2n2 + 1 n=1 5" c. S 3" + 2 n= In(n) 1 D. Σ (Hint: Try comparing this to n2 n3/2 n=3 n=3 I MIMO Ε.Σ sin (1) (Hint: Try comparing this to n n=1 n=1
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
1. Provide a complete and accurate e-N proof that the following sequences converge. That is, prove these sequences converge n-+2 (b) an= n-cos(n) 4n2-7 Tn (d) { } 2. Prove that the following sequences diverge. (Def 7.10 pg 596) READ Sequences that Diverge to oo or-oo (b) ann infinity. Hint: Provide an M -N proof that an approaches 1. Provide a complete and accurate e-N proof that the following sequences converge. That is, prove these sequences converge n-+2 (b) an=...