Question: 2. Let (an)2 1 be a sequence with positive terms, such that lim an+1 = 2023. Show that lim an = 00. an Hints: Recall

2. Let (an)2 1 be a sequence with positive terms, such that lim an+1 = 2023. Show that lim an = 00. an Hints: Recall that lim On = L, when for every & > 0 there exists an integer N such that I-E N. Use this definition to show that there exists an integer N such that ant1 2 an for all n > N. - Suppose that (an) , is bounded above. Can you then conclude something about its limit? - Apply the Algebraic Limit Theorem to anti . ] an

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!

Please help with the following questions: The Ratio Test. CK) Suppose that Z on is a series with positive terms, and lim on" = L (L could be 00). ":1 "Ir>00 an :0 o If L 1 then the series 2 an is...

Symbolic answers must be entered using notation similar to the examples given below. If you enter decimal numbers for questions that indicate that a symbolic answer is required, it will be marked as...

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...

Recall that N is the set of positive integers and Q is the set of rational numbers. NOTE: "Limit point\Sequences - Part 2 (Week 4) Infinite Limits Definition. A sequence (sn) is said to diverge to +...

Fraction of hosts infected Case Study 2 Hosts, Parasites, and Time-Travel 0.8 0.6 0.4 0.2 0 Past Contemporary Future Time Figure \u00031 Horizontal axis is the time from which the parasite was taken,...

Convex geometry 0.1 Dehn-Sommerville relations In this section we will talk about convex polytopes. One possible denition of a convex polytope uses the notion of a half-space: A closed half-space in...

Sections 10.1 and 10.2 Reading Assignment: Sequences and Series Answer Only Exercise 1, 2, and 3 by using a screenshot provided Calculus Pearson textbook. Make sure you read these three questions...

KINDLY PLEASE DIGITALIZED IT 11- Find the Area between the curve y=x(x-3) and the ordinates x=0 and x=5. Note: (hint) The Graph shows 2 regions. Get first the area of each region before adding it...

Kindly please digitalized the answer 1- Integrate the following. 1. fx'dx 2. JT 3. S(x2 - 2x + 5) dx 4. S(x + 2)5 dx 5. S1+ y2 2ydy 6. S cos(70 + 5) do 7. S ( x2 + 2x - 3)(x + 1) dx 11- Find the Area...

The following CFG is in Chomsky normal form. The table below is a partially filled CYK table for determining if the string aabbcc is in the language of this grammar. 1 10 La 5 C 1 A 2 S AY | AC | BX...

Example 1 used measured performance IQ scores for three different blood lead levels. If we use the same three categories of blood lead levels with measured verbal IQ scores, we get the accompanying...

A factory employs 5 0 workers, each paid a basic hourly rate of R 5 5 . 0 0 for a 3 5 - hour working week. Overtime is paid at R 7 5 . 0 0 per hour. It takes each employee 3 hours to produce one unit...

A hula hoop and solid disc of equal radii are rolled, from rest and without slipping, down an incline plane. Which one will reach the bottom of the inclined plane first? Explain.

Methods of Estimating Costs-Account Analysis: The accounting records of a company indicate the following manufacturing costs were incurred in Year 1: These costs were incurred to produce 50,000 units...

Methods of Estimating CostsAccount Analysis: The accounting records of a company report the following manufacturing costs for the past year: Production was 70.000 units. Fixed manufacturing overhead...

Methods of Estimating Costs-High-Low Cost: During the past five years, operations at a company have remained relatively stable. Over this time, the following data are available from the accounting...