Sequence monotonic homework problem help

In summary, the given sequence is increasing and unbounded. This is determined by analyzing the behavior of the sequence as n gets larger. As n approaches infinity, the sequence continues to increase without bound, making it both increasing and unbounded.
  • #1
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Homework Statement



Consider the sequence.

http://www.webassign.net/cgi-bin/symimage.cgi?expr=a_n = 4 n + 1/n

(a) Determine whether the sequence is increasing, decreasing, or not monotonic.

(b) Is the sequence bounded?



Homework Equations





The Attempt at a Solution



I got the answer to a and that is increasing

I am not sure about (b). How do I find that out??
 
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  • #2


Bounded means, it will reach a point where it will stop increasing more and more quickly. For example, if you had just 1/x^2, it will get smaller and smaller and smaller until the increment is tiny and the sum of the sequence will end up converging to a number.

your sequence is 4n + 1/n ... therefore, as n gets bigger and bigger, what will happen? try it out with increasingly big numbers to see the trend. if it keeps getting bigger faster and faster, then its UNBOUNDED.
 
  • #3


rekshaw said:
Bounded means, it will reach a point where it will stop increasing more and more quickly. For example, if you had just 1/x^2, it will get smaller and smaller and smaller until the increment is tiny and the sum of the sequence will end up converging to a number.
A sequence {sn} is bounded if there are numbers M and N such that M <= sn <= N for all n = 1, 2, 3, ...
 
  • #4


Yes it does keep on increasing. It doesn't stop. But I am not sure if it's faster and faster or not. I know it keeps getting bigger. So it's unbounded? And what about (a) increasing?
 
  • #5


You have an = 4n + 1/n, which has no upper bound. A sequence is increasing if an + 1 >= an for all n >= 1. (Some texts use the phrase strictly increasing if an + 1 > an.)
 

1. What is a sequence monotonic homework problem?

A sequence monotonic homework problem is a type of mathematical problem that involves determining whether a given sequence of numbers is monotonic, meaning that it either constantly increases or decreases. The problem typically involves analyzing the pattern of numbers and determining if it follows a specific rule or trend.

2. How do I solve a sequence monotonic homework problem?

To solve a sequence monotonic homework problem, you will need to carefully analyze the given sequence of numbers and determine if there is a constant increase or decrease. This can be done by calculating the difference between each consecutive number and observing the overall trend. You may also need to use algebraic equations or formulas to help determine the pattern.

3. What are some tips for solving a sequence monotonic homework problem?

Some tips for solving a sequence monotonic homework problem include carefully examining the given sequence, looking for any patterns or trends, and using algebraic equations or formulas to help determine the pattern. It may also be helpful to try different approaches or methods to see which one works best for the specific problem.

4. Are there any common mistakes to avoid when solving a sequence monotonic homework problem?

Yes, some common mistakes to avoid when solving a sequence monotonic homework problem include misreading or misinterpreting the given sequence, not considering all possible patterns or trends, and making errors in calculations or equations. It is important to double-check your work and carefully analyze the problem before reaching a solution.

5. How can I check if my solution to a sequence monotonic homework problem is correct?

The best way to check if your solution to a sequence monotonic homework problem is correct is to verify if it follows the given sequence and satisfies the conditions of being monotonic. You can also use mathematical tools such as graphs or tables to visually represent the sequence and check if your solution is accurate.

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