Question: Prove that for any real sequence {xn}. lim sup x,-inf sups) and liminfAn = sup ( Infxk 1+00

Prove that
Prove thatfor any real sequence {xn}.

for any real sequence {xn}.

lim sup x,-inf sups) and liminfAn = sup ( Infxk 1+00

Step by Step Solution

★★★★★

3.54 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

It suffices to prove the first identity Let s inf n N sup k n x k Case 1 s Then sup k n x k for al... 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

Document Format (1 attachment)

Word file Icon

741-M-N-A-D-I (212).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Q:

For any real sequence define a) Prove that if lim infkxk > x for some x R, then xk > x for k large. b) Prove that if xk x as k , for some x R, then lim infk xk = x. c) If ak > 0 for all k N, prove...

Q:

Let C be a fixed, positive constant. If {bn} is a sequence of nonnegative numbers that converges to 0, and {xn} is a real sequence that satisfies |xn - a|

Q:

Suppose that {xn} is a real sequence. Prove that and -lim supXp = lim inf(-rn) lim inf x-lim supt-x)

Q:

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

Q:

Recall that N is the set of positive integers and Q is the set of rational numbers. NOTE: "Limit point\Sequences - Part 2 (Week 4) Infinite Limits Definition. A sequence (sn) is said to diverge to +...

Q:

A) Let {xn } be a bounded sequence. Prove directly using the denition of lim inf and lim sup that there exists two possibly dierent subsequences {xnk } and {xnk } of {xn } where lim inf xk = lim xnk...

Q:

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

Q:

Given that xn is bounded a sequence of real numbers, and given that an = sup{xk: k n} and bn = inf{xk: k n), let the lim sup xn = lim an and lim inf xn = lim bn. Prove that if xn converges to L,...

Q:

Suppose that {xn} and {yn} are real sequences. a) Prove that provided that none of these sums is of the form - . b) Show that if limn xn exists, then and c) Show by examples that each of the...

Q:

MAT1325 : Homework #2 Prof : Monica Nevins Due Thursday, February 4, 2016 by 9pm at the Department of Mathematics and Statistics (KED) Staplers are not available at the Department. Instructions : sh...

Q:

A glass flask whose volume is 1000.00 cm3 at 0.0oC is completely filled with mercury at this temperature.When flask and mercury are warmed to 55.0oC, 8.95 cm3 of mercury overflow. If the coefficient...

Q:

It appears that Allen can earn at least its current level of income for the indefinite future Based on this information the investors think that an appropriate investment capitalization rate for...

Q:

You invest $ 2 , 6 0 0 and get a return of 8 . 2 % per year. You have to pay a fee of 5 bps per year. Now, how much will you have after 1 1 years ( simple annual compounding ) ? Your Answer:

Q:

(Reasons for International Specialization) What determines which goods a country should produce and export?

Q:

4. Define ak recursively by a1 = 1 and k>1. Prove that 2:%"=1 ak converges absolutely.

Q:

3. Using Exercise 9, p. 135, prove that 00 (_1)k x2k+1 smx = L (2k I)! k=O + 00 (_1)kx2k and cos x = L (2k)! k=O for all x E [0, IT /2J.

Q:

2. Decide, using results covered so far in this chapter, which of the following series converge and which diverge. 00 k2 00 k' (a) Lk (b) L 2~ (c) {00; (k2k+ +1 3 r (d) ~ (IT -~) k- 1. k=l IT k=l 00...

Q:

A change in expected inflation affects both the supply and demand for bonds. True/False A change in the interest rate does not shift the demand for bonds. True/False 3. An increase in the expected...

Q:

Ghost, Inc., has no debt outstanding and a total market value of $185,000. Earnings before interest and taxes, EBIT, are projected to be $29,000 if economic conditions are normal. If there is strong...

Q:

attach excel in the answer QM0.2 a) The following table shows bets for several companies. Calculate each stock's expected rate of return in CAPM. Assume the risk free rate of interestis 9 percent....