Proving 139/159 is Not an Upper Bound for E = {(14n + 11)/(16n + 19): n ε N}

[teme92]

Homework Statement

Prove that 139/159 is not an upper bound for the set of real numbers:

E ={(14n + 11)/(16n + 19): n ε N}


Homework Equations

The Attempt at a Solution

Right so I let 14n + 11 = 139 and I got n=9.14. Since n is supposed to be natural and the answer I got for n isn't, can I deduce that 139/159 is not an upper bound for E?

 

[shortydeb]

You have to find a positive integer such that if you plug it into (14n + 11)/(16n + 19) you get a number greater than 139/159.


 

[teme92]

Hey shortydeb thanks for the quick reply.

That is what I originally thought but do I not need to get a number n that lies before and after 139/159 but not exactly on it? Its very tedious work if that is the case :/

 

[shortydeb]

Set (14n + 11)/(16n + 19) equal to 139/159 and see what you get for n.

 

[Ray Vickson]

Hey shortydeb thanks for the quick reply.

That is what I originally thought but do I not need to get a number n that lies before and after 139/159 but not exactly on it? Its very tedious work if that is the case :/

No. All you need do is find an integer n giving the fraction > 139/159. You do not need to find the "best" or "nearest" n, or anything like that.

 

[teme92]

Ok I get it now so. Thanks for the help much appreciated