My Math Forum How do you determine the sequence is bounded above or bounded below?

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 October 18th, 2016, 03:44 PM #1 Newbie   Joined: Oct 2016 From: San Francisco Posts: 4 Thanks: 0 How do you determine the sequence is bounded above or bounded below? Given a calculus sequence, how to find if the function is bounded above or below?
 November 20th, 2016, 04:39 PM #2 Newbie   Joined: Nov 2016 From: New Zealand Posts: 1 Thanks: 0 When you have the graph, it's easier. If the function exists on the point you're looking at, and the line's coming from above, then it's bounded from above. And vice versa.
 November 21st, 2016, 09:41 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 No, one can answer this question in general, how you do that depends strongly upon the given series! For example, if the sequence were $\frac{n- 1}{n+1}$, the first thing I notice is that all numbers are positive so 0 is a lower bound. Further, this is a fraction with numerator n-1 and denominator n+ 1. Obviously n-1< n+ 1 so the numerator is always less than the denominator. That means the fraction is always less than 1 and 1 is an upper bound.
November 21st, 2016, 09:59 AM   #4
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 Originally Posted by Country Boy No, one can answer this question in general, how you do that depends strongly upon the given series! For example, if the sequence were $\frac{n- 1}{n+1}$, the first thing I notice is that all numbers are positive so 0 is a lower bound. Further, this is a fraction with numerator n-1 and denominator n+ 1. Obviously n-1< n+ 1 so the numerator is always less than the denominator. That means the fraction is always less than 1 and 1 is an upper bound.
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# determination of bounded function below and above

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