Suppose that a series an has positive terms and its partial sums Sn satisfy the inequality

Question:

Suppose that a series ∑ an has positive terms and its partial sums Sn satisfy the inequality Sn ≤ 1000 for all n. Explain why ∑ an must be convergent.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0538497909

7th edition

Authors: James Stewart

See More Books

Question Posted: Mar 04, 2016 07:26 AM

See More Questions

Suppose that a series o an has positive terms and its partial sums s n satisfy the inequality s n < 1000 for all n. Explain why a n must be convergent.
Suppose an and bn are series with positive terms and bn is known to be convergent. (a) If an > bn for all n, what can you say about an? Why? (b) If an < bn for all n, what can you say about an? Why?
Suppose an and ba are series with positive terms and bn is known to be convergent. (a) If an > bn for all n, what can you say about an? Why? (b) If an < bn for all n, what can you say about an?...
Using the sinking fund Table 13.3, complete the following: Note: Do not round intermediate calculations. Required amount $ Frequency of Length of payment time 8 years 15,000 Annually Interest rate 8...
Recall from Chapter 3 that enterprise architecture describes the blueprint of the information technology and organizational resources that are used to execute business processes. At what stage in the...
Which attributes from the College Scorecard data would you need to compare the percentage of students who receive federal loans at universities above and below the median cost of attendance across...
The technique of marginal costing can be a valuable aid to management. Discuss.
The physical distribution channel of a major food manufacturer consists of plant stocks from which regional warehouses are restocked. These regional warehouses in turn supply the field warehouses...
FIN385 - Fall 2017 Spreadsheet Project #2 Ticker: ECL Template generated for: Company: Ecolab Inc. Fiscal Year Ending Assets Debt Shares Revenue EBIT Interest NetInc Stock Price Tax Paid Tax rate...
Shady Lady sells window coverings to both commercial and residential customers. The following information relates to its budgeted operations for the current year. The controller, Kelly Swenson, is...
If an is divergent and c ( 0, show that can is divergent.
The Cantor set, named after the German mathematician Georg Cantor (1845-1918), is constructed as follows. We start with the closed interval [0, 1] and remove the open interval (1/3, 2/3). That leaves...
Regarding IRC Section 107, how many annotations are listed in the following services? a. Standard Federal Tax Reporter, Commerce Clearing House b. United States Tax Reporter, Research Institute of...
Evaluate the following integrals:
Example: Evaluate each of the following: In(1+m) (a) e cos(1-e)dx 10- (b) [Int] -dt sec(3P)tan (3P) (c) 12 2+ sec(3P) dP (d) cos(x)cos(sin(x))dx (e) dw W 50 20
a) Describe the following concepts in the context of organizational development. b) Discuss how these concepts interrelate and support each other within an organizational framework
Q2. a) Analyze the importance of communication in the change management process. b) Suggests strategies that a Disaster Management Organization can employ to ensure effective communication during...
Compare the results of Problem 4.2 with direct BPF expansion of the exact time domain output by estimating the mean integral square error (MISE). Plot the exact solution along with the two BPF...
(a) With not more than 300 words, examine why Malaysia missed its 2020 targets to divert 40% of waste from landfills and increase recycling rates to 22%. (10 marks) b) Why arent Malaysian recycling?...
ETHICS AND INVENTORIES. Mary Cravens is an accountant for City Appliance Corporation. One of Marys responsibilities is developing the ending inventory amount for the calculation of cost of goods sold...
Evaluate the line integral, where C is the given space curve. Scy dx + z dy + x dz, C: x = Vi, y= t, z= t, 1 <1 <4 %3D
A vector field F and a curve C are given. (a) Show that F is conservative and find a potential function f. (b) Evaluate C F dr using Theorem 2. (c) Evaluate C F dr by first replacing C with a...
Evaluate the surface integral. ls x ds, S is the surface y = x? + 4z, 0
You borrowed $15,000 for buying a new car from a bank at an interest rate of 12% compounded monthly. This loan will be repaid in 48 equal monthly installments over four years. Immediately after the...
Discuss how debt restructuring, settlement, or modification works. Discuss the journal entries for debtor and creditor
Could CNL be a viable business? If so, under what conditions and what level of production (and, since production is directly related to production workers, employees)? All information provided for...

Suppose that a series an has positive terms and its partial sums Sn satisfy the inequality

Question:

Step by Step Answer:

The partial sums S n form an increasing sequence sin...View the full answer

Calculus Early Transcendentals

Students also viewed these Calculus questions