How to Determine if a Sequence is Bounded using the Definition: Example with a_n = 1/(2n + 3)

How to Determine if a Sequence is Bounded using the Definition: Example with a_n = 1/(2n + 3)

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Thank you:)

[JRazek]

Can we assume in this proof for the sake of simplicity M=1?

If I understood correctly - the def. of bounded sequence is the following:
exists M: such that for any natural n>0: a(n) <= M

Therefore we can choose any M that meets the requirements.

If we chose M=1:
1/(2n+3) <= 1 | *(2n+3) [it is positive]
1 <= 2n+3
2n+2 >= 0
n+1 >= 0
end of proof.

[calculus]

Thanks sir .. i was finding difficult is proving a monotonic sequence

[Fjgrugnn]

I‘m a student from Germany and these videos in English explain so much better than the German ones AND I DONT KNOW WHY (excuse my poor English)

[joshual]

Thank you ! I was confused what the meaning behind bounded was

[cristinaleon]

Thank you! What if it’s bounded only above or below?

[yt_]

Is the sequence: 1, 1, 1/2, 1, 1, 1, 1/2 a bounded sequence?