Question: Let M in R and let (sn) be a sequence satisfying both of the following conditions: i. sn0, the set {n in N: |sn-M|

Let M in R and let (sn) be a sequence satisfying both of the following conditions: i. sn0, the set {n in N: |sn-M|<} is infinite. Prove that lim supsn = M

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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

Students Have Also Explored These Related Mathematics Questions!

Derive Shepardis lemma and use it to show that the Slutsky matrix is symmetric. ... Assignment 1.pdf (1 page) 1 3 Q Q Search CAS EC 501 Microeconomics Assignment 1 Due 2/11/20 1. NS 3.4 (" As we saw...

answer the question clearly You are building a flight-control system for which a convincing safety case must be made. Would you assign the tasks of safety requirements engineering, test case...

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...

Python and most Python libraries are free to download or use, though many users use Python through a paid service. Paid services help IT organizations manage the risks associated with the use of...

Show that if

ret Electricity consumers are supplied with electricity from an electricity generating station. Electricity is distributed from the station to the various consumers through a network of transformers...

Could someone please check my work and let me know if I am correctly using all of the included theorems that are referenced in the proof Please state all definitions and theorems that you will need:...

commentthecaseofKeriChisolm,ofCostaMesa,California.DescribethereasonsforherdisciplineandhowitreflectsonhercompetenceasaCPA. pdf page 19 UPDATE SPRING/SUMMER 2016 ISSUE NO. 81 PRESIDENT'S MESSAGE One...

Hi, I am in difficulty when I kept trying to do these questions. Could you give me a help to solve these questions? Thank you so much. Note: I attach the extra information as well Q1 (7 points) 4-l-1...

Quantity supplied 7,200 Price, $ Quantity demanded 210 800 1.80 1,00 4,800 1.60 2,400 2,400 140 3,200 800 1.20 4.100 200 The table above shows the demand and supply schedule for a football ticket....

Emma, a U.S. resident, received the following income items for the current tax year. Identify the source of each income item as either U.S. or foreign. a. $600 interest from a savings account at a...

can multiple projects be allocated to a hierarchy of sub - customers in QuickBooks online

uppose that X has a Binomial(n, p) distribution, where 0