Question: Prove the Root Test Take any number such that L whenever n ( N. (i) If then use series is absolutely convergent (and therefore convergent)?

Prove the Root Test Take any number such that L whenever n ( N.
(i) If then use series is absolutely convergent (and therefore convergent)?
(ii) If 1 or then the series is divergent?
(iii) If the Root Test is inconclusive?

lim-=L

Step by Step Solution

★★★★★

3.44 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

i Following the hint we get that a n r n for n N and so since the geometric series ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

786-C-I-S (210).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

a) Prove that the Root Test applied to the series yields r = 1. Use the Logarithmic Test to prove that this series converges. b) Prove that the Ratio Test applied to the series yields r = 1. Use...

Prove that F(x) = L [f(x) - L] = 0. lim lim

Prove that for any positive integer n, 2 52-

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

1.) Determine whether the series is absolutely convergent, conditionally convergent or divergent. (-1)n-1 4vn n=1 7n + 1 Part 1: Test _ lanl The series _ lanl ? ? Justification: converges diverges O...

Section 10.5 Reading Assignment: Absolute Convergence; The Ratio and Root Tests Answer Only Exercise 1, 2, and 3 by using a screenshot provided Calculus Pearson textbook. Make sure you read these...

1.) Determine whether the series is absolutely convergent, conditionally convergent or divergent. (-1)"(6n) n=1 V16n4 - 1 Part 1: Test _ lanl The series _ lanl converges Justification: O A. By the...

Series - Ratio and Root Tests: Problem 13 (1 point) Use the Root Test to determine the convergence or divergence of the given series or state that the Root Test is inconclusive. i\": ( n + 15 )" ":1...

Can you help me with those questions pls Determine whether the series is absolutely convergent, conditionally convergent, or divergent: 712" 2 (8") 71:1 The series is ? Preview My Answers You have...

list Evaluate the following integral K dx 2 + 4x + 20 Question 1 Question 2 dx 2 + 4X + 20 tan * + C (Type an exact answer.) O Question 3 O Question 4 O Question 5 Question 6ng thuc chinh... (14)...

Quasars are thought to be the nuclei of active galaxies in the early stages of their formation. A typical quasar radiates energy at the rate of 1041 W. At what rate is the mass of this quasar being...

The downtown core of Gotham City consists of one-way streets, and the traffic flow has been measured at each intersection. For the city block shown in Figure 2.19, the numbers represent the average...

E2.9 (LO 2, 3) (Adjusting Entries) Selected accounts of Leno Company are shown below. Supplies Accounts Receivable Beg. Bal. 800 10/31 470 10/17 2,100 10/31 1,650 Salaries and Wages Expense Salaries...

Personal Assets In his role as a promoter for a new business, Spence purchased an employment agency from Huffman. The new corporation never generated enough money to pay Huffman. As a result, Huffman...

Evaluate the integral. e- cos 20 de

Evaluate the integral.

Evaluate the integral. x tan?x dx

1. First City Bank pays 7 percent simple interest on its savings account balances, whereas Second city bank pays 8 percent interest compounded annually. IF you made an $8000 deposit in each bank, how...

Find the bank discount and the proceeds for the following; assume 360 days: Maturity Value Discount Rate Time (days) Bank Discount Proceeds $8,000 3% 120 $4,550 8.1% 110 $19,350 12.7% 55 $63,400 10%...

REPLACEMENT ANALYSIS The Bigbee Bottling Company is contemplating the replacement of one of its bottling machines with a newer and more efficient one. The old machine has a book value of $625,000 and...