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October 18th, 2016, 04:44 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, 05:39 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, 10:41 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
No, one can answer this question in general, how you do that depends strongly upon the given series! For example, if the sequence were , the first thing I notice is that all numbers are positive so 0 is a lower bound. Further, this is a fraction with numerator n1 and denominator n+ 1. Obviously n1< 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, 10:59 AM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 2,202 Thanks: 1157  Quote:
 

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