Bounding and Monotonic Thm Problem

[francisco300]

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

a_n= 1/(2n +3)

I can tell by writing out a1, a2, etc that the upper bound is 1/5 and the lower bound is 0 but I do not know how to go about proving it. I only have two examples to go from and they both include a_n inside itself so the assumptions are easier to do. Any tips?

 

[pka]

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

a_n= 1/(2n +3)

Clearly that sequence is decreasing and because each term is positive it is bounded.
Prove by induction.

 

[francisco300]

How would I go about doing that? I am looking at 1/a_n = b_n which should be > 5. Can proving that b_n increases be enough to show that a_n is decreasing?

 

[stapel]

How would I go about doing that?

Are you asking how to do induction proofs? Or have you attempted an induction proof, and got stuck? If the former, please study one or two lessons (at least!) at the link. If the latter, please reply showing your work. Thank you!