Consider the sequence: {an = ln (2n? +n) – In(n? +10)}. (1) Give a, and a2...
Find the limit of the sequence whose nth term is 2n + ln(n) An= 5n Show all of your work. Hint. Use l'Hospital's Rule.
Determine whether the sequence an = ln(2n + 1) - In(n +2) converges or diverges, and if it converges, find the limit. Find the length of the curve defined by x = 2t3, y = 3t2, osts 1.
Prove: without using l'hopital's rule. infinity 2n-1 ln(2) (2n-1) n infinity 2n-1 ln(2) (2n-1) n
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
2. Consider the following sequence x(n) = cos (2n/3)sin(2ton/5). a. Is the sequence periodic? If yes, what is the period? If no, why not? Note: you need to show your work analytically but you can verify that your answer is correct by sketching the sequence using Matlab b. Find and sketch the complex exponential Fourier series coefficients (Magnitude and Phase). Verify using Matlab. Include code and graphics.
(1 point) Consider the sequence ax ncos(n) 2n-1 Write the first five terms of a,, and find liman. If the sequence diverges, enter"divergent" in the answer box for its limit. a) First five terms: b) lim,-- ..
2n +10 Determine (without using a calculator) whether or not the series Σου Sn +n is convergent. Find its limit if it is convergent a
1. Consider the sequence defined recursively by ao = ], Ant1 = V4 an – An, n > 1. (a) Compute ai, a2, and a3. (b) For f(x) = V 4x – x, find all solutions of f(x) = x and list all intervals where: i. f(x) > x ii. f(x) < x iii. f(x) is increasing iv. f(x) is deceasing (c) Using induction, show that an € [0, 1] for all n. (d) Show that an is an increasing...
Let Consider the geometric series M-1 (-1)^-1 got7 Sm = Enci (1) Give S2 (-1)n-1 21+1 gon (2) What area and r of the this geometric series? (3) Determine algebraically (without using a calculator) if the series is convergent or divergent and why. (4) Find the sum algebraically if it is convergent.
Write out the first five terms of the sequence with, \(\left[\frac{\ln(n)}{n+1}\right]_{n=1}\), determine whether the sequence converges, and if so find its limit. Enter the following information for \(a_{n}=\frac{\ln (n)}{n+1}\). \(a_{1}=\) \(a_{2}=\) \(a_{3}=\) \(a_{4}=\) \(a_{5}=\) \(\lim_{n \rightarrow \infty} \frac{\ln (n)}{n+1}=\) (Enter DNE if limit Does Not Exist.) Does the sequence converge (Enter "yes" or "no").