Question: Let an = (n), where is a continuous, decreasing function such that (x) 0 and Data From Exercise 81 Let an

Let an = ƒ (n), where ƒ is a continuous, decreasing function such that ƒ (x) ≥ 0 andS. f(x) dx.

Assume an converges to S. Arguing as in Exercise 81, show that n=1 Conclude that M n=1 M+1 Sme f(x) dx 5 [


Data From Exercise 81

Let an = ƒ (n), where ƒ is a continuous, decreasing function such that ƒ (x) ≥ 0 andS. f(x) dx.

Show that

Sf(x) dx s f(x) dx an a + n=1 f f(x) f(x) dx


S. f(x) dx.

Step by Step Solution

★★★★★

3.48 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Following the proof of the Integral Test and the argument in Exercise 81 but st... View full answer

blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!

Q:

Let an = f (n), where f (x) is a continuous, decreasing function such that f (x) ¥ 0 and Show that f(x) dx converges. f(x) dx

Q:

Compose a detailed paper about Leadership: Part one requires you to compare and contrast Trait Leadership Theory with Situational Leadership, highlighting the advantages and disadvantages of both...

Q:

Your company produces a sports magazine. In 2020, it's first year in operation, it sold $169,000 of one-year subscriptions, of which only 50% had expired by December 31, 2020. In 2021, it sold...

Q:

Student: allan cranford Date: 9/7/16 Instructor: Basu Dipanker Course: MAT-240-Q6622-16EW6 Assignment: 1-3 MyStatLab: Module One Problem Set 1. The following data represent the percent of owners of...

Q:

( Please explain both A and B ) I think A is not coding and B is . Question 1 . Taylor Polynomials Engineers and physicists frequently use the approximation sin ( x ) x for x small, which is a first...

Q:

Use the Divergence Test to determine whether the following series diverges or state that the test is inconclusive. k K = 0 3k + 1 . . . Select the correct answer below and fill in the answer box to...

Q:

(5) (Something useful) In this problem we are going to produce an important continuous real- valued function on the Moore Plane T. For each e > 0 and x R, let B((x,0), e) be the T-basic neighborhood...

Q:

I have tried using mgf/cdf/convolution methods to proof part ii and iii. However, I always get stuck at the end. I hope someone can guide me on how to show the proofs. Any help would be greatly...

Q:

answer all questions as instructed below. make sure you have attended all questions .Comparative Architectures (a) Describe the organisation of a two-level branch predictor that makes use of a global...

Q:

Throughout the class, youve learned many ways in which the study of derivatives can be applied to business operations. The last unit covers some additional topics that will come up again in later...

Q:

Add. Reduce to lowest terms and write as whole or mixed numbers if appropriate. 1/4 + 11/12 + 7/16

Q:

The series converges to 5/4. Calculate SN for N = 1, 2, . . . until you find an SN that approximates 5/4 with an error less than 0.0001. 1213

Q:

Explain the difference between macroeconomics and microeconomics. Give examples of the areas of concern to each branch of economics.

Q:

What is the difference between the demographic and behavioral bases of market segmentation?? LOP85

Q:

Complete the following sentences. a. A function is continuous from the left at a if _________. b. A function is continuous from the right at a if _________.

Q:

If lim xa f(x) = L and lim xa +f(x) = M, where L and M are finite real numbers, then how are L and M related if lim xa f(x) exists?

Q:

Describe the end behavior of f(x) = -2x 3 .

Q:

You will notice that PepsiCo's portfolio has included (or currently includes) such companies as Wilson Sporting Goods, North American Van Lines, Frito-Lay, Taco Bell, KFC, Pizza Hut and Quaker Oats....

Q:

Lucy, Max and Mark are partners in a contracting business (a partnership) which cannot pay its debts. Lucy owns 50%, Max owns 25% and Mark owns 25%. Under Joint and Several Liability creditors can...

Q:

Majestic Corporation is planning a 12-year project that will have an initial cost of $900,000. During the first 3 years, there will be cash inflows of $80,000. Years 4-10 will see cash inflows of...