Question: Show, directly from the definitions, if a > 0 and the sequence (an)-1 converges to a, then the sequence (an/3)=1 converges to a 1/3.

Show, directly from the definitions, if a > 0 and the sequence

Show, directly from the definitions, if a > 0 and the sequence (an)-1 converges to a, then the sequence (an/3)=1 converges to a 1/3. [Suggestion: Use the identity (x^3 - y^3) = (x - y) (x^2 + xy + y^ 2).

Step by Step Solution

★★★★★

3.49 Rating (159 Votes )

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 Accounting Questions!

If X is a hypergeometric rv, show directly from the definition that E(X) = nM/N (consider only the case n

Show directly from the time-independent Schrdinger equation that (p 2 ) = (2m[E - V(x)]) in general and that (p 2 ) = (2mE) for the infinite square well. Use this result to compute (p 2 ) for the...

Show directly from the definition that the following are not Cauchy sequences. (a) ((-1)n, (b) n + (-1)n/n), (c) (ln n)

Beam ABCD is supported by a pin at A and a straight bar DE. The beam is subject to a distributed load q=10 kN/m in the AC section, and a concentrated moment Mo=40 kN-m at C. The beam has a length of...

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

this is the file for the previous quesions so ill just add $15 to this one and you can claim the other one as well cause they are not letting me cancel it \fForm 1040 2014 (99) Department of the...

file tax form for filing jointly with married couple with children CORRECTED (if checked) PAYER'S name, street address, city or town, state or province, country, ZIP or foreign postal code, and...

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...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

The following transactions were selected from those occurring during the month of January 2014 for Dans Store Inc. A wide variety of goods is offered for sale. Credit sales are extended to a few...

You are the senior accountant in the audit of Granger Grain Corporation, whose business primarily involves the purchase, storage, and sale of grain products. The corporation owns several elevators...

A peculiar mipect of software and sofinare - elated products is product pricing related to sevalable tealures. For example, tas preparation software comes in two or tree versions: basic, enhanced and...

In the circuit shown in Fig. both batteries have insignificant internal resistance and the idealized ammeter reads 1.50 A in the direction shown. Find the emf E of the battery. Is the polarity shown...

Show that the rth moment about the origin of the gamma distribution is 3( ) 3*T(a ()

For a chi-squared distribution find X 2 .such that (a) P(X 2 > X 2 ) = 0.99 when v = 4; (b) P(X 2 > X 2 ) = 0.025 when v = 19: (c) P(37.652

Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 60.00. If dog A exerts a force of 270 N and dog B exerts a force of300 N, find the magnitude of the resultant...

Illustrated in the figure is a 1 ½ -in-diameter steel countershaft that supports two pulleys. Pulley A delivers power to a machine causing a tension of 600 lbf in the tight side of the belt...

A researcher wants to test whether the math score of students in Town A is higher than that of students in general. The mean math score of students in Town A is 100, the mean math score of students...

Burt Baskin and Irv Robbins began making ice cream in 1945. Initially they developed 31 flavors-one for each day of the month. (Source: Baskin- Robbins) a) How many 2-dip cones are possible using the...

Kayla sold a total of 145 Italian sausages and hot dogs from her curbside pushcart and collected $242.05. She sold 45 more hot dogs than sausages. How many of each did she sell? CENTR

Complete the following table. Initial Investment at ibling Amount Interest Doubling Rate, kTime, T t0, P After 5 Years a) $35,000 b) $5000 c) d) e) $109,000 f) 3.296 : . $7,130.90 $9,923.47 11 years...

A person on a bridge throws a rock straight down toward the water. The rock has just been released? Describe a situation. For each, draw a motion diagram, a force-identification diagram, and a...

A bag of groceries is on the seat of your car as you stop for a stop light. The bag does not slide. Draw a motion diagram, a force-identification diagram, and a free-body diagram for the bag?

A spring-loaded gun shoots a plastic ball. The trigger has just been pulled and the ball is starting to move down the barrel. The barrel is horizontal? Describe a situation. For each, draw a motion...