theorems of analysis  
 
  L'Hospital's rule  
 
  Integration techniques  
 
  Taylor expansions  
 
  Constants  
 
  home  
 
  ask us  
 

 
      Calculus II

      Contents




© The scientific sentence. 2010

Calculus II: Sequences



Exercises

A sequence is a list of numbers written in a specific order.

The infinite sequence has an infinite number of terms.

The general term of a sequence is denoted as an and the serie as {an}

1. Write the three first terms and the 10th term of the following two infinite sequences:

a)     {(n + 1)/n2}

b)    {(-1)n+1. 2n+1}

2. Write the sequence {1/√n} as a function and graph this function.
What i sthe limit of this function when n tends to ∞ ?.

3.

The Squeeze Theorem for Sequences tells us:

For three sequences {an}, {bn}, and {cn} with an ≤ bn ≤ cn for all sufficiently large n

If

lim an = lim cn = L
n → ∞ n → ∞

Then

lim bn = L
n → ∞


     an = {(n + 1)2/n2}
    bn = {(n + 2)/n}
    cn = {((n + 1)/n}


Apply this theorem to show that

lim bn = 1
n → ∞



Solutions








  


chimie labs
|
Physics and Measurements
|
Probability & Statistics
|
Combinatorics - Probability
|
Chimie
|
Optics
|
contact
|


© Scientificsentence 2010. All rights reserved.