Question: Let an > 0 and suppose that (an converges. Prove that (an2 converges?

Let an > 0 and suppose that (an converges. Prove that (an2 converges?

Step by Step Solution

★★★★★

3.41 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Since a n converges Thus there is some positive integ... 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

955-M-C-D-E (2522).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

Let an > 0 and suppose that an converges. Construct a convergent series bn with bn > 0 such that lim(an/bn)= 0; hence bn converges less rapidly than an. [Let (An) be the partial sums of an and A its...

Q:

For n ¥ 1, let f n be real-valued measurable functions defined on an open set E R containing 0, and suppose that | f n ( x )| £ M (

Q:

Let (an) be a decreasing sequence of real numbers converging to 0 and suppose that an diverges. Construct a divergent series bn with bn > 0 such that lim(bn/an)= 0; hence bn diverges less rapidly...

Q:

Could someone please check my work 2. Prove Corollary 4.2.5. If (in) converges TO T and T, 20 for all nEIN, Then T20. Suppose (tn) converges to t and tn 2 0 for all n E N. Let Sn = (0, 0, 0, ...) ,...

Q:

............. (4) Consider the sequence of functions (fn) defined by fn(x) = nx 1+nx for x 2 0. (a) Find the pointwise limit f(x) = limn > fn(x) for x 2 0. (b) Let a > 0. Prove or disprove: (fn)...

Q:

Let A be a non-empty set, and let /: AA be a function. Suppose that f is bijective. Suppose further that A is finite; the results in this exercise are valid only for finite sets. Let x, y A. (3)...

Q:

A positive decreasing function f defined in (0,1] and a variable c>=0 such that the integral from 0 to 1 of (x^c)*f(x) converges Prove that the limit when x approaches 0 from the right of (x^ (c+1))*...

Q:

Prove that P is a polytope. Let M, C R" is a nonempty polytope, M, C R" is a nonempty polyhedron. Let P = Min M2. Suppose that P # 0. ~ Prove that P is a polytope

Q:

Suppose that {an} converges. Prove that {a^2 n} converges.

Q:

Write down your proof of the "Monotone Convergence Theorem:" that every bounded monotone(-decreasing) sequence converges (to its infimum). Here's the google doc we worked on together.(Links to an...

Q:

Consider the following game tree representing a simple dollar auction game. The following describes the extensive-form game in detail. THE PLAYERS: Bidders 1 and 2, each with a wealth level of $3....

Q:

Briefly describe the insurance company ratings assigned by A. M. Best, Moodys, Fitch, and Standard & Poors. Why is it important to know how a company is rated? What ratings would you look for when...

Q:

Sandra and Kelsey are forming a partnership. Sandra will invest a piece of equipment with a book value of $ 4 , 4 0 0 and a fair market value of $ 1 3 , 8 0 0 . Kelsey will invest a building with a...

Q:

Distinguish between a firms fixed costs and variable costs and give an example of each.

Q:

In another alternative model, called the Ricker model, the per capita production decreases exponentially. Suppose that per capita production is Our models of bacterial population growth neglect the...

Q:

In a model with an Allee effect, organisms reproduce poorly when the population is small. In one case, per capita production follows Our models of bacterial population growth neglect the fact that...

Q:

Sketch graphs of the above function. f(x) = x / x + 1 for 0 x 2 For Information: (the updating function in Section 1.5, Exercise 23).

Q:

A researcher was interested in examining the relationship between middle school students' sports activity and sex. They summarized the data they collected in a two-way table. The data collected are...

Q:

Q. 2. A winery maintains a dataset containing information about customers who subscribe to its tasting events and special offers for wine cases. The winery occasionally mails tasting to send samples...

Q:

XYZ stock price and dividend history are as follows: Year Beginning-of-Year Price Dividend Paid at Year-End 2010 $ 118 $ 3 2011 $ 126 $ 3 2012 $ 110 $ 3 2013 $ 115 $ 3 An investor buys six shares of...