Let (left{R_{n}ight}_{n=1}^{infty}) be a sequence of real numbers such that (R_{n}=oleft(n^{-1}ight)) as (n ightarrow infty). Prove that

Question:

Let $\left\{R_{n}ight\}_{n=1}^{\infty}$ be a sequence of real numbers such that $R_{n}=o\left(n^{-1}ight)$ as $n ightarrow \infty$. Prove that $R_{n}^{2}=o\left(n^{-1}ight)$ as $n ightarrow \infty$.

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

Step by Step Answer:

Related Book For answer-question

Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

See More Books

Question Posted: Mar 15, 2024 11:01 PM

See More Questions

Solve the inequalities, expressing the solution sets as intervals or unions of intervals. Also, show each solution set on the real line. |x| < 2
Calculate S 3 , S 4 , and S 5 and then find the sum of the telescoping series 00 n=1 1 n+1 1 n+ 2
Write an SQL statement to display all columns of all rows of PET. Do not use theasterisk (*) notation. 3.2 Write an SQL statement to display the breed, type, and DOB of all pets having the type Dog....
Find the deflection y(x) of a cantilever beam embedded at its left end and free at its right end when the load is as given in Example 10.
What kind of attraction pulls electrons close to the atomic nucleus?
Given A = x2 _ y3 + z1 and B = xBx + y2 + zBz: (a) Find Bx and Bz if A is parallel to B; (b) Find a relation between Bx and Bz if A is perpendicular to B.
What is the default filename that make will process if no other is given?
You have been asked to audit Greystone Company. During the course of your audit, you are asked to prepare comparative data from the company's inception to the present. You have determined the...
Using concepts from Appendix B on the accompanying CD with this book on the DDM and this chapter, answer the following questions. (a) Derive an expression for the P/E ratio in terms of the pay out...
Suppose that $v_{1}(\alpha)$ and $v_{2}(\alpha)$ are constant with respect to $n$. Prove that if $R_{n}=\left[n^{-1 / 2} v_{1}(\alpha)+n^{-1} v_{2}(\alpha)+o\left(n^{-1}ight)ight]^{2}$ then a...
Prove Theorem 7.8. That is, let $\left\{X_{n}ight\}_{n=1}^{\infty}$ be a sequence of independent and identically distributed random variables from a distribution $F$. Let \(F_{n}(t)=P\left[n^{1 /...
Of the four imperatives discussed in this chaptereconomic, political, quality, and administrationwhich would be most important to IBM in its efforts to make inroads in the Pacific Rim market? Would...
Should the US pursue an isolationist foreign policy, or should it continue to be active on the global stage? Why?
What sectors are driving new recruitments in the UAE?
What can a HIPS do that a NIPS cannot? (Choose two.) Detect malware delivered to the host via an encrypted channel. Protect a mobile host while connected to non-secured networks. Block malware as it...
Why is it necessary to wear organisation-approved, brightly coloured, waterproof band- aids to cover cuts and abrasions?
4. What is the difference in metrics used by the following router protocols: distance vector and link state? 5. How did Classless Inter-Domain Routing (CIDR) help alleviate the problem of too many...
The beam AB has a negligible mass and thickness and is subjected to a triangular distributed loading. It is supported at one end by a pin and at the other end by a post having a mass mp and...
Find the area of the surface generated by revolving the para- metric curve x = cos 1, y = sin? 1 (0 < I sa/2) about the y-axis.
Suggest an example of a product and a competitive situation where it would not be profitable for a firm to spend large sums of money to establish a brand.
List five brand names and indicate what product is associated with the brand name. Evaluate the strengths and weaknesses of the brand name.
Explain family brands. Should Best Buy carry its own dealer brands to compete with some of the popular manufacturer brands it carries? Explain your reasons.
A solar panel dealer acquires a used panel for $13,000, with terms FOB shipping point. Compute total inventory costs assigned to the used panel if additional costs include $5,500 for sales staff...
You are given three capacitors and need to arrange them in the following circuit. The battery has a potential of 3 0 volts. You have one of each type of capacitor: 2 0 mf , 5 0 mf , 8 0 mf What...
What is the horizontal reaction force at the support point A? 20 kips 12 kips 10 kips 15'-0" 15'-0" 15'-0" 15'-0" 15'-0" 60'-0" 8 kips THAT B

Let (left{R_{n}ight}_{n=1}^{infty}) be a sequence of real numbers such that (R_{n}=oleft(n^{-1}ight)) as (n ightarrow infty). Prove that

Question:

Step by Step Answer:

Introduction To Statistical Limit Theory

Students also viewed these Business questions