Suppose that ak > 0 for k large and that k=1 ak/k converges. Prove that ak lim

Question:

Suppose that ak > 0 for k large and that ˆ‘ˆžk=1 ak/k converges. Prove that

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

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 04:05 AM

See More Questions

Let {ak} and {bk} be real sequences. Decide which of the following statements are true and which are false. Prove the true ones and give counterexamples to the false ones. a) If k=1 ak converges and...
Suppose that ak 0. Prove that k=1 ak converges if and only if the series k=1 (a2k + a2k+1) converges.
Suppose that ak > 0 and that ak1/k as k . Prove that k=1 akxk converges absolutely for all |x| < 1/a if a 0 and for all x R if a = 0.
Once down to about 15, the worlds only wild flock of whooping cranes now numbers a record 237 birds in its Texas Coastal Bend wintering ground (www.SunHerald.com). The average whooping crane egg...
Mr. Sam Golff desires to invest a portion of his assets in rental property. He has narrowed his choices down to two apartment complexes, Palmer Heights and Crenshaw Village. After conferring with the...
Is there a common law duty to rescue someone in distress? a. Under what conditions does such a duty exist? Give an example.
Consider the regression model in Problem 3.43. The value of the adjusted $R^{2}$ is Data From Problem 3.43 You have fit a linear regression model with three predictors to a sample of 50 observations....
The plane wall with constant properties and no internal heat generation shown in the figure is initially at a uniform temperature T i Suddenly the surface at x = L is heated by a fluid at T having a...
The following information pertains to ABC Corporation: Beginning raw materials inventory $37,000 Ending raw materials inventory $45,000 Beginning work-in-process inventory $18,000 Ending...
Wholesome Dairy processes milk. The cost of the milk processing is $1,250,000. Wholesome is looking to increase its net income and is exploring the possibility of expanding its products to include...
A series k=0 ak is said to be Cesdro summable to an L R if and only if converges to L as n . a) Let sn = n-1k=0 ak. Prove that for each n N. b) Prove that if ak R and k=0 ak = L converges, then...
If nk=1 = kak = (n + 1)/(n + 2) for N, prove that 34
How do inclination and elevation determine the use of a satellite?
Compare Statement 1 and Statement 2 and identify which best explains the view of a speculative volatility trader and which best explains the view of a hedger of volatility. Justify your response....
In Nowackis backtesting of the factor-based strategy for the new fund, the calculated information coefficient should be based on: A. FS(t) and SR(t). B. FS(t) and SR(t 1). C. SR(t) and FS(t 1)....
The most appropriate trading strategy for the sell order of Music Plus shares is: A. trading in the open market. B. selling at the closing auction for the day. C. passive trading over the course of...
To fill the remaining portion of the ABC order, Yellow is using: A. an arrival price trading strategy. B. a TWAP participation strategy. C. a VWAP participation strategy. Robert Harding is a...
Recommend a solution that will provide the fund manager the opportunity to earn currency alpha through active foreign exchange management. Gupta and the fund manager of Portfolio A discuss the...
Human exposure to the electromagnetic radiation in air is regarded as safe if the power density is less than 10 mW/m 2 . What is the corresponding electric field intensity?
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate. tan 0.8035
Continuation of Exercise 5-61. Determine the following: (a) Marginal distribution of X (b) Joint distribution of X and Y (c) Conditional probability distribution of X given that Y = 0.5 and Z = 0.5...
The yield in pounds from a days production is normally distributed with a mean of 1500 pounds and standard deviation of 100 pounds. Assume that the yields on different days are independent random...
The weights of adobe bricks used for construction are normally distributed with a mean of 3 pounds and a standard deviation of 0.25 pound. Assume that the weights of the bricks are independent and...
The following table shows the data from 2000 general social survey. The table cross classifies gender and political party identifications. Subjects indicated whether they identified more strongly...
The Information Richness of Communication Media The four types of communication media are Face-to-face Communication, Spoken Communication Electronically Transmitted, Personally Addressed Written...
Once you've chosen your company or product, explain why you would not purchase from that company or that product. Be sure to give an argument making use of moral principles to support your statements.

Suppose that ak > 0 for k large and that k=1 ak/k converges. Prove that ak lim

Question:

ak lim

Step by Step Answer:

Let 0 and choose N so large that kN1 a k k 2 ...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions