Q. 6 Determine whether the following sequences converge or diverge, and state whether they are monotonic...
(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 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 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)
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)
3. If the series 2-1 bn is converge, determine whether the series - converge or diverge! 4. A right triangle ABC with the angle at A is and the length of the side |AC|=b. The side CD, EF, FG, etc is perpendicular to AB, while DE, FG, etc is perpendicular to BC as shown below: G E с As you can see the length 1CD to DE, to IEF, to |FG|, etc is getting smaller and smaller. Using the picture...
3. If the series 2-1 bn is converge, determine whether the series - converge or diverge! 4. A right triangle ABC with the angle at A is and the length of the side |AC|=b. The side CD, EF, FG, etc is perpendicular to AB, while DE, FG, etc is perpendicular to BC as shown below: G E с As you can see the length 1CD to DE, to IEF, to |FG|, etc is getting smaller and smaller. Using the picture...
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
3. Determine if the following sequences converge or diverge. Show work. (1){1/27 +(3/87")"} (b) {(2/3)* + 1")"}
State whether the following series converge absolutely, converge conditionally, or diverge. Clearly state the reasons for your answers 2n (a) 3n 72
1 sin )-sin Determine whether the following series converge or diverge. +1 Select one a. Diverges b. Converges, and the partial sum is 1 C. Converges, and the partial sum is sin 1 2 d. Converges, and the partial sum is 0