3. Evaluate using the correct form -dx 0 x-2 4. Consider the sequence 3n n+1 Does...
1 2 3 n-9n2 1. Consider an = 1+ 2n - 5n2 (a) (3 points) Does the sequence {an} converge or diverge? Show your work. (b) (3 points) Does the series an converge or diverge? Why? 2. (8 points) Use a comparison test to state whether the given series converges or diverges. 3. (6 points) Does the given series converge or diverge? If it converges, what is its sum? § (cos(n) – cos(n + 1))
Does sigma (3n^2-n+1)/sqrt(n^7+2n^2+5) converge or diverge using limit comparison test.
Consider the sequence: -2/3, 2/9, -2/27, 2/81, -2/243……Part 1: A Formula Find a formula for the nth term of this sequence:an = _______ ∑Part 2: Limit of the Sequence Find the limit of the sequence: lim(n->∞) an = _______ ∑Remember: INF, -INF, DNE are also possible answers. Part 3: Converge or Diverge? Does this sequence converge or diverge?
Consider the series (n=1 and infinite) ∑(−1)^(n+1) (x−3)^n / [(5^n)(n^p)], where p is a constant and p > 0. a) For p=3 and x=8, does the series converge absolutely, converge conditionally, or diverge? Explain your reasoning. b) For p=1 and x=8, does the series converge absolutely, converge conditionally, or diverge? Explain your reasoning. c) When x=−2, for what values of p does the series converge? Explain your reasoning. (d) When p=1 and x=3.1, the series converges to a value SS....
2. Consider the sequence {2(-1)"}=1 (a) List the first 4 terms. (b) Compute for the partial sum of SA (e) Determine if the series converge or diverge. If it does converge what value it converges to. 00 2-3) nal
4. For: 1 + x3 dx a) Evaluate I using the trapezoidal rule with n= 4. (15 pts) b) Evaluate I using the 1/3 Simpson's rule with n=2. (10 pts) Trapezoidal Rule Single Application 1 = (6-a) f(b) + f(a) Composite (b-a) 2n I= i=1 Simpson's 1/3 Rule Single Application Composite b) Evaluate I using the 1/3 Simpson's rule with n=2. (10 pts) Trapezoidal Rule Single Application f(b) + f(a) I = (b-a) 2 Composite I = (b − a)...
Suppose q is a constant and q> 4. 2"(n + 1)! (a) (5 marks) Does the sequence {an}, where an = – -, converge or diverge? Justify your answer. 2(n+1)! (b) (6 marks) Does the series - converge or diverge? Justify your answer and state the name(s) of any test(s) you used.
show all work | 2n-1) 2. Consider the sequence |(n+1)! a) is the sequence monotone increasing or monotone decreasing or neither? b) Find upper and lower bounds for the sequence. c) Does the sequence converge or diverge? (Explain) 3. Determine if the series converges or diverges. If it converges, find its sum. => [-1-] c) Ë ?j? – 1-1 j? +1
Does the series converge or dliverge? 1. nel n Does the series converge absolutely, converge conditio 2. n-2 vn-1 3nn! 3. Does the series converge or diverge? 2-6.10.(4n+ 2) Does the series converge or diverge? 4. 2 nln n Does the series converge or dliverge? 1. nel n Does the series converge absolutely, converge conditio 2. n-2 vn-1 3nn! 3. Does the series converge or diverge? 2-6.10.(4n+ 2) Does the series converge or diverge? 4. 2 nln n