20. Show that 20 shows that Siſi-1). either converges or does not converge.
(10 pts) Does the following series converge or diverge? If it converges, then to what does it converge? 2.4"-2 1-15"-3
Determine if the Sequence converges or diverges for an= (3n2+1)/4n2; what does it converge to?
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
Does the following series converge absolutely, converge conditionally or diverge? jo (-1)4+1 27k diverges converges absolutely converges conditionally Box 1: Select the best answer For the series below calculate find the number of terms n that must be added in order to find the sum to the indicated accuracy. 2 (-1)"+1) 2n3 +4 error] < 0.01 n= Preview Find the sum of the series correct to 2 decimal places. Sum = Preview Box 1: Enter your answer as a number...
Given the series: 9 k k=1 does this series converge or diverge? converges diverges If the series converges, find the sum of the series: k Preview (If the series diverges, just leave this second box blank.)
QUESTION 2 The improper integral e-*dx converges to e b.-e-1 d. The integral does not converge. ADRIAN
Claim: {(-1)"} does not converge to any real number a. Proof: Assume that the sequence converges; that is, assume that there is an a E R such that lim,--.(-1)" = a. Then, using E = 1, from the definition of convergence, we know that there exists an no such that |(-1)" - al < 1 for all n > no. Thus, for any odd integer nno, we have |(-1)" - al = 1-1-a[< 1, and for any even integer n>...
QUESTION 2 The improper integral s** e-Xdx converges to a. The integral does not converge. b. O c. 1 e d.-e-1
(3) Prove that the sequence fn (x(max10,z - n))2 does not converge uniformly on IR, but converges uniformly on compact subsets of R (3) Prove that the sequence fn (x(max10,z - n))2 does not converge uniformly on IR, but converges uniformly on compact subsets of R
does the series converge or diverge and why? If it converges find a sum. (2b) lim 1c. Does the following si in (n+3) lim In(n+3) nyo n+3 lim nt3 2 (2 points). If the terms of a se converge? Why or why not? have to be O. An example 3 (4 points). Does the series co 2a. § 8(9)"=3 n = 1 26. I 2 k = k + 6k+8 4 (2 points). If the terms of a se Why...