Let (left{x_{n}ight}_{n=1}^{infty}) and (left{y_{n}ight}_{n=1}^{infty}) be a sequences of real numbers such that (x_{n} leq y_{n}) for all

Question:

Let $\left\{x_{n}ight\}_{n=1}^{\infty}$ and $\left\{y_{n}ight\}_{n=1}^{\infty}$ be a sequences of real numbers such that $x_{n} \leq y_{n}$ for all $n \in \mathbb{N}$. Prove that

\[\liminf _{n ightarrow \infty} x_{n} \leq \liminf _{n ightarrow \infty} y_{n}\]

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

See More Books

Question Posted: Mar 15, 2024 02:01 AM

See More Questions

Let $\left\{x_{n}ight\}_{n=1}^{\infty}$ and $\left\{y_{n}ight\}_{n=1}^{\infty}$ be a sequences of real numbers such that $x_{n}>0$ and $y_{n}>0$ for all $n \in \mathbb{N}$, \[0
Let $\left\{x_{n}ight\}_{n=1}^{\infty}$ and $\left\{y_{n}ight\}_{n=1}^{\infty}$ be a sequences of real numbers such that \[\left|\limsup _{n ightarrow \infty} x_{n}ight|
An investment will pay you $4803.69 in 2 years if you pay $2298.16 today. What is the implied rate of return?
Identify a true statement about the rational and emotional aspects of leadership. Multiple choice question. Leadership is not about the rational or emotional sides of human experience Leadership...
On a fishing trip you catch a 2.77-lb bass, a 14.3-lb rock cod, and a 13.43-lb salmon. What is the total weight of your catch?
More frequent compounding What is the relationship between the number of compounding periods per year and present values? What about future values? Why do these relationships exist?
8-4. Cul es la diferencia entre datos secundarios y primarios ?
Pan-Am Manufacturing Company prepares cost estimates for projects on which it will bid. In order to anticipate the labor cost to be included in a request to bid on a contract for 1,200,000 units that...
If you are going to receive $70,000 for 20 years starting 5 years from now, what is the present value of the cash flows discounted at 12%?
Let $\left\{f_{n}(x)ight\}_{n=1}^{\infty}$ and $\left\{g_{n}(x)ight\}_{n=1}^{\infty}$ be sequences of real valued functions that converge pointwise to the real functions $f$ and $g$,...
Let $\left\{x_{n}ight\}_{n=1}^{\infty}$ be a sequence of real numbers. a. Prove that \[\inf _{n \in \mathbb{N}} x_{n} \leq \liminf _{n ightarrow \infty} x_{n} \leq \limsup _{n ightarrow \infty}...
1. Intercompany profit elimination entries in consolidation workpapers are prepared in order to: a Nullify the effect of intercompany transactions on consolidated statements b Defer intercompany...
Lennys Limousine Service (LLS) is considering the purchase of two Hummer limousines. Various information about the proposed investment follows: Required: Help LLS evaluate this project by calculating...
Lancer Corp. has the following information available about a potential capital investment Required: 1. Calculate the projects net present value. 2. Without making any calculations, determine whether...
Woodchuck Corp. is considering the possibility of outsourcing the production of upholstered chair pads included with some of its wooden chairs. The company has received a bid from Padalong Co. to...
Woodchuck Corp. is considering eliminating a product from its line of outdoor tables. Two products, the Oak-A and Fiesta tables, have impressive sales. However, sales for the Studio model have been...
Suppose that Flyaway Company also produces the Windy model fan, which currently has a net loss of $$40,000$ as follows: Eliminating the Windy product line would eliminate $$20,000$ of direct...
Ciano Landscaping Company uses the allowance method to account for its uncollectible accounts. Three years ago, it wrote off a $ 40,000 account due from Haber Incorporated. Haber paid this account in...
What are the risks and liability factors in an audit? What are the implications to the auditor? What are the implications to the organization? How can the auditor mitigate these risks and liability...
Suppose that Karen and John get together to grade their students exams. The time required for Karen to grade a question on a students exam is normally distributed with mean 90 seconds and standard...
Suppose two parents have blood genotypes such that the probability that any of their children have blood type A is 0.75. a. If they have 5 children: i. What is the probability that all have blood...
Reconsider Exercise 11.8.20. Describe how the probability that ((p(vector) Kayla p(vector) Jose > 0) would change if: a. The sample sizes were larger. b. Kaylas probability of successfully making a...
Given that rJ = 6.3%, rRF = 4.1%, and rM = 9.4%, determine the beta coefficient for Stock J that is consistent with equilibrium.
Simon Companys year-end balance sheets follow. At December 31 2017 2016 2015 Assets Cash $ 33,019 $ 37,839 $ 38,623 Accounts receivable, net 93,822 65,556 54,152 Merchandise inventory 117,963 89,253...
PLEASE REFER TO THE 2018 ANNUAL REPORT OF STARBUKS FOR THE YEAR FISCAL YR 2018, ENDING SEPTEMBER 30, 2018. Refer to the management discussion & analysis section and write a one page summary...

Let (left{x_{n}ight}_{n=1}^{infty}) and (left{y_{n}ight}_{n=1}^{infty}) be a sequences of real numbers such that (x_{n} leq y_{n}) for all

Question:

Step by Step Answer:

To prove that liminfn to infty xn leq liminfn to infty yn we can use the fo...View the full answer

Introduction To Statistical Limit Theory

Students also viewed these Business questions