Calculus Exercise

[liru92]

Hello
{n^3-4n^2}n=1 till + infinity

Show that the given sequence is eventually strictly increasing or eventually strictly decreasing

 

[Deleted member 4993]

Hello
{n^3-4n^2}n=1 till + infinity

Show that the given sequence is eventually strictly increasing or eventually strictly decreasing

Since you are stuck in the starting point, let's start with definitions and properties?

What is the definition of strictly increasing/decreasing sequence? What are the properties of strictly increasing/decreasing sequence? - i.e. how would know one - if you saw one of those functions?

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

 

[liru92]

Since you are stuck in the starting point, let's start with definitions and properties?

What is the definition of strictly increasing/decreasing sequence? What are the properties of strictly increasing/decreasing sequence? - i.e. how would know one - if you saw one of those functions?

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

First of all sorry cause I'm new here.
So. I am an university student.
So I started this exercise like an+1-an=-(3n^2+5n+5) then I don't know what to do !

 

[stapel]

{n^3-4n^2}n=1 till + infinity

Show that the given sequence is eventually strictly increasing or eventually strictly decreasing

What does the equality mean? You have an algebraic expression on the left-hand side, which is set equal to a puzzling phrase ("one plow, plus infinity"??) on the right-hand side.

What is the exact text of the exercise? What are the precise instructions?

I started this exercise like an+1-an=-(3n^2+5n+5)

What does this mean? What are you "starting", and why? What is the point of the "1" on the left-hand side (since an-an = 0)?

We can't see your book or your assignment. You'll need to tell us what you're talking about.

 

[Deleted member 4993]

First of all sorry cause I'm new here.
So. I am an university student.
So I started this exercise like an+1-an=-(3n^2+5n+5) then I don't know what to do !

I assume you mean,

a_n+1 - a_n = -(3n² + 5n + 5) How did you get that from a_n = (n³ - 4n²)*n

I do not get that. Please show work.

 

[DrPhil]

First of all sorry cause I'm new here.
So. I am an university student.
So I started this exercise like an+1-an=-(3n^2+5n+5) then I don't know what to do !

a little problem of interpretation .. let me try to rewrite the question:

"Consider the sequence a_n = (n^3 - 4n^2), for n --> infinity
Show that the given sequence is eventually strictly increasing or eventually strictly decreasing."

That is, for large enough n, the sign of [a_{n+1} - a_n] is either always + or always -.

So you expanded the powers of (n+1) in the a_{n+1} term, and then subtract a_n.
Please check your work - especially the signs. All terms in (n+1)^3 are positive, and all therms in -4(n+1)^2 are negative.

 

[HallsofIvy]

Since you title this "Calculus Exercise" did you consider finding the derivative and using that?