Suppose that ak 0 as k . Prove that a sin(2k + 1)x) !

Question:

Suppose that ak †“ 0 as k †’ ˆž. 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 04:07 AM

See More Questions

Suppose that {ak} and {bk} are real sequences such that ak 0 as k , Prove that k=1 akbk converges. 1ak +1-akl < oo, and !
Suppose that ak 0 as k . Prove that given Îµ > 0 there is a Î´ > 0 such that for all x, y [0, 1] which satisfy |x - y| 0
Let {ak} and 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 ak is strictly decreasing...
Report Format Market analysis Business - Pizza Vending Machine - Target Place : Universities 1. Target Market University Students in the UK University food 2. Potiential Customers 3. Barrier of entry...
You are asked to evaluate the following two projects for the Norton Corporation. Using the net present value method combined with the profitability index approach described in footnote 2 of this...
The Floreses kids wanted to go to college in Florida because they loved the beaches. Correct any apostrophe errors in the above sentence. Write your correction. If a sentence is correct, write C.
French and Schultz ("Water Use Efficiency of Wheat in a Mediterranean-type Environment, I The Relation between Yield, Water Use, and Climate," Australian Journal of Agricultural Research, 35, 743-64)...
Here are earnings per share for two companies by quarter from the first quarter of 2009 through the second quarter of 2012. Forecast earnings per share for the rest of 2012 and 2013. Use exponential...
How is General Electric case using analytics for process improvement?
There is a lottery with n coupons and n people take part in it. Each person picks exactly one coupon. Coupons are numbered consecutively from 1 to n, n being the maximum ticket number. The winner of...
Prove that converges for every x (0, 2Ï) and every ak 0. What happens when x = 0? o0 cost
For each of the following series, let sn represent its partial sums and s its value. Prove that s is finite and find an n so large that sn approximates s to an accuracy of 10-2. a) b) c)...
The demand for a new product is estimated to be normally distributed with = 200 and = 40. Let x be the number of units demanded and find the following probabilities: a. P(180 x 220) b. P(x 250)...
Find one solution for each of the difference equations below: (a) $y(n)+2 y(n-1)+y(n-2)=0, y(0)=1$ and $y(1)=0$ (b) $y(n)+y(n-1)+2 y(n-2)=0, y(-1)=1$ and $y(0)=1$.
If boys and girls are equally likely, groups of 400 births have a mean of 200 girls and a standard deviation of 10 girls. Is 232 girls in 400 births an unusually high number of girls?
Reconsider Problem 44 using an incremental present worth analysis. Data from problem 44 Dark Skies Observatory is considering several options to purchase a new deep-space telescope. Revenue would be...
Given a linear time-invariant system, prove the properties below: (a) A constant group delay is a necessary but not sufficient condition for the delay introduced by the system to a sinusoid to be...
We define the even and odd parts of a sequence $x(n), \mathcal{E}\{x(n)\}$ and $\mathcal{O}\{x(n)\}$ respectively, as \[\begin{aligned}\mathcal{E}\{x(n)\} & =\frac{x(n)+x(-n)}{2}...
The electric field intensity of a uniform plane wave in free space is given by E = 40 cos(t z)a x + 60 sin(t z)a y V/m (a) What is the wave polarization? (b) Determine the magnetic field intensity.
Presented below are income statements prepared on a LIFO and FIFO basis for Kenseth Company, which started operations on January 1, 2024. The company presently uses the LIFO method of pricing its...
Construct a normal probability plot of the visual accommodation data in Exercise 6-5. Does it seem reasonable to assume that visual accommodation is normally distributed?
Construct a normal probability plot of the O-ring joint temperature data in Exercise 6-13. Does it seem reasonable to assume that O-ring joint temperature is normally distributed? Discuss any...
Construct a normal probability plot of the octane rating data in Exercise 6-14. Does it seem reasonable to assume that octane rating is normally distributed?
How do I use voice commands to control my computer with the project of making a video?
Dan Mullen is employed by a mail-order distributor and reconditions used desktop computers, broadband routers, and laser printers. Dan is paid $12 per hour, plus an extra $6 per hour for work in...
Consider two series Yt and Y2t: Y = IIY-1 +6 Or more explicitly as: Aye Aya Yit Elt + Y2t 2t in which = [1, 2]' is IID with E(e) = 0 and E(ee'): [ 0 0 a) Write the system in levels Answer: A-AU-N b)...

Suppose that ak 0 as k . Prove that a sin(2k + 1)x) !

Question:

a sin(2k + 1)x) に!

Step by Step Answer:

By a sum angle formula and telescoping we see that 2 sin x n k1 sin2k 1x n k1 ...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions