1. Show that the following sequences converge to 1, by calculating an-1 in each case: (b)...
(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
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)
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=...
Compare the solutions the results in I(d) and 2(d). to Show that the following sequences converge linearly to p 0. How large must n be before Ip -pl s 10- p" =-, ,121 1t a Show that for any positive integer k, the sequence defined by pa 1/n converges linearly to For each pair of integers k and m. determine a number N for which i/Nk<10m 8. a. Show that the sequence p, 10converges quadratically to 0. Show that the...
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) {
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
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
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
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)