Thread: Showing the sequence is bounded.

Hey all i thought i understood this question, but after having another look i think my solution is wrong.

"Show that the sequence {an} is bounded, where an, is given by

"

I know what if i show {an} is convergent, then it is therefore bounded.

My initial idea was to show that an was convergent by the alternating series test.

But thats the problem, its not a series.
So is my method correct, or shall i be approaching this differently?

Thanks for your help!

What am I missing?

Originally Posted by Plato

What am I missing?

Why did u just take the absolute value of an?
And i dont get what your asking me?

Originally Posted by simpleas123

Why did u just take the absolute value of an?
And i dont get what your asking me?

I don't get what it is that you do not understand.
Do you understand what it means to be bounded?

Originally Posted by Plato

I don't get what it is that you do not understand.
Do you understand what it means to be bounded?

Ahh, its so simple!

For some M.
In this case, being that an converges to 1 therefore M = 1.

Thank you very much!

Originally Posted by simpleas123

Ahh, its so simple!

For some M.
In this case, being that an converges to 1 therefore M = 1.

Thank you very much!

does not converge to 1.

Leave alone for a moment the statement: "If is convergent then it is bounded".


Boundedness is a concept that comes before convergence,


"A sequence is bounded if there is a number M such that

for all n.


Convergence has nothing to do with boundedness so far.


Thats why Plato did what he did.