1. (10 pts) Determine whether the given series converges or diverges. Be sure to justify your...
Determine whether the given series converges or diverges. Fully justify your answe(a) \(\sum_{n=2}^{\infty} \frac{1}{\sqrt{n} \ln n}\)(b) \(\sum_{n=1}^{\infty} \cos \left(\frac{1}{n^{2}}\right)\)(c) \(\sum_{n=1}^{x} \frac{(2 n) !}{5^{n} n ! n t}\)
3) Determine whether the given series converges or diverges. i) (7 pts.] 4n2 + 3η +1 2n2 - η n=2 ii) (8 pts.] Σ 2n 11 COS NI iii) (10 pts.) ΠΕ1
30) Determine whether the series converges absolutely, converges conditionally, or diverges. Be sure to indicate which test you are applying and to show all of your work. (The final exam may include different series that require different convergence tests from the test required in these problems) 3" 2" c) b) n-1 n 2"n e)Σ d) n-2川Inn (2n 30) Determine whether the series converges absolutely, converges conditionally, or diverges. Be sure to indicate which test you are applying and to show...
Determine whether the series converges or diverges. n = 1 converges diverges
Determine whether the following series converges. Justify your answer. 8 + cos 10k Σ k= 1 Select the correct answer below and, if necessary, fill in the answer box to complete your choice. (Type an exact answer.) 8+ cos 10k 9 O A. Because 9 E and, for any positive integer k, E converges, the given series converges by the Comparison Test. 8 k=1 00 OB. The Integral Test yields f(x) dx = so the series diverges by the Integral...
Problem 2. Determine whether the sequence { "" } converges or diverges. Justify your answer.
se a convergence test of your choice to determine whether the following series converges or diverges. 002 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The Ratio Test yields r = This is greater than 1, so the series diverges by the Ratio Test. O B. The terms of the series are alternating and their limit is so the series converges by the Alternating Series Test. OC. The Ratio...
1. Determine whether the series converges or diverges.$$ \sum_{k=1}^{\infty} \frac{\ln (k)}{k} $$convergesdiverges2.Test the series for convergence or divergence.$$ \sum_{n=1}^{\infty}(-1)^{n} \sin \left(\frac{3 \pi}{n}\right) $$convergesdiverges
Use the integral test to determine whether the series converges. Show all work to justify your answer. vands n=1 Select one: O A. diverges O B. converges
8-31 Determine whether the series - converges or diverges. If it converges, find the sum. (If the quantity diverges, enter DIVERGES.) Son 8-31 n=1 - = nsion Determine whether the series converges absolutely, conditionally, or not at all. (-1) - 1 n1/2 n=1 The series converges absolutely. The series converges conditionally. The series diverges. For which values of x does (n + 4)!x converge? n = 0 (-0,00) (-1,1) O no values exist O x = 0 (-4,4) Find the...