Suppose that a n is a series with positive terms. Prove that if a n converges,
Question:
Suppose thatΣ an is a series with positive terms. Prove that if Σ an converges, then Σ sin an also converges.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 62% (8 reviews)
Because lim a 0 the terms ...View the full answer
Answered By
Hradayesh singh
Detail-oriented professional tutor with a solid 5 years of experience instilling confidence in high school and college students. Dedicated to empowering mathematics students and civil engineer with constructive feedback and practical test-taking strategies. Effective educator and team player whether working in a school, university, or private provider setting. Active listener committed to helping students overcome academic challenges to reach personal goals.
Unparalleled interpersonal communication and listening skills, whether working with students, parents, teachers, or administrators. -Deep background
Teach efficient testing techniques and methods for managing stress.
Conduct timed practice exams to help students feel comfortable with the testing process.
Evaluate students’ progress and adjust instruction based on feedback.
0.00
0 Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Let a n be a series with positive terms and let r n = a n+1 /a n . Suppose that lim n r n = L < 1, so a n converges by the Ratio Test. As usual, we let Rn be the remainder after n terms, that is, R n...
-
Prove that each of the following series converges and find its value, a) b) c) d) (-1)k-1 7 9k-1 COSR 5-3
-
Prove that if (an is convergent series of positive terms then (In (1 + an) converges?
-
In 2020/21 Ella had taxable income (after deducting the personal allowance) of 52,000, all of which represented savings income. She paid 1,600 as a Gift Aid donation to the NSPCC (a registered...
-
With constant tax rates over time, why does a single premium deferred annuity contract (SPDA) provide greater after tax rates of return than does a money market account? How is the difference in...
-
What drivers of a social entrepreneurs business plan would lead to grant funding? Debt? Equity?
-
What are some of the best practices to manage information security and privacy in terms of procedural, technical, and physical controls?
-
Joanne is a seventy-five-year-old widow who survives on her husbands small pension. Joanne has become increasingly forgetful, and her family worries that she may have Alzheimers disease (a brain...
-
Norsk Optronics, ALS, of Bergen, Norway, had a current ratio of 4 on June 3 0 of the current year. On that date, the company s assets were: Cash $ 6 6 , 0 0 0 Accounts receivable, net 4 0 0 , 0 0 0...
-
George Littlechild started a new kitchen and bath design business called Littlechild Enterprises. The following activities occurred during its first month of operations, March 2014: a. Littlechild...
-
In Exercises use the result of Exercise 53 to approximate the sum of the convergent series using the indicated number of terms. Include an estimate of the maximum error for your approximation. Data...
-
In Exercises (a) Use Theorem 9.5 to show that the sequence with the given th term converges (b) Use a graphing utility to graph the first 10 terms of the sequence and find its limit. Data from in...
-
Derive a centered finite difference formula for the second derivative using four evaluation points.
-
At a given point in the high-speed flow over an airplane wing, the local Mach number, pressure, and temperature are 0.7, \(0.9 \mathrm{~atm}\), and \(250 \mathrm{~K}\), respectively. Calculate the...
-
Air enters a smooth, insulated circular duct at $M=3$. Determine the stagnation pressure loss in the duct for $\mathrm{L} / \mathrm{D}=20$ and 40 . Take $f=0.02$.
-
In the infinitesimal neighborhood surrounding a point in an inviscid flow, the small change in pressure, \(d p\), that corresponds to a small change in velocity, \(d V\), is given by the differential...
-
Self-employed workers in the United States must pay Social Security taxes equal to 12.4% of any income up to \($118,500\) in 2015. This income level of \($118,500\) is known as the cap. Income in...
-
Suppose that the production function is Y = 9K 0.5 N 0.5. With this production function, the marginal product of labor is MPN = 4.5K 0.5 N -0.5 . The capital stock is K = 25 The labor supply curve is...
-
From the elements position on the periodic table, predict the electron configuration of each atom. a. Cl b. K
-
Write the expression in radical notation. Then evaluate the expression when the result is an integer. 23 -1/2
-
In the definition of the logarithmic function, the base a is not allowed to equal 1. Why?
-
The concentration of alcohol in a persons bloodstream is measurable. Suppose that the relative risk R of having an accident while driving a car can be modeled by an equation of the form R = e kx...
-
San Francisco in 1906: seismographic reading of 50,119 millimeters 100 kilometers from the center. In problem use the following discussion: The Richter scale is one way of converting seismographic...
-
The following information is available for Avatar Company: Raw materials inventory Work in process inventory Finished goods inventory Materials purchased Direct labor Sales revenue Sales discounts...
-
Calculations Marketing Inc. issued 11.0% bonds with a par value of $540,000 and a five-year life on January 1, 2020, for $605,699. The bonds pay interest on June 30 and December 31. The market...
-
The year-end 2021 balance sheet of Brandex Incorporated listed common stock and other paid-in capital at $2,600,000 and retained earnings at $4,900,000. The next year, retained earnings were listed...
Study smarter with the SolutionInn App