Recent content by elizaburlap

Okay! Thanks!

This is why I thought that the greatest lower bound was one. Because n=1, 1/n=1. as far as I know n cannot be smaller than one as a natural number. Doesn't this make 1 the greatest lower bound??

Well, I thought it was, because x has to be a natural number.

Homework Statement Find the least upper bound and greatest lower bound (if they exist) of the following sets and state whether they belong to the set: a. {1/n:n\in"Natural Number"} b. {x\in"Rational Number":0≤x≤√5 c. {x irrational:√2≤x2} d. {(1/n)+(-1)n:n\in"Natural Number"}...

How would you go about extending it to infinity? In the text it has a few examples that span n from 1 to infinity. Such as, an=n(-1)^n I understand that it does converge, because an approaches 0 as n approaches infinity, but when the equations become more complicated, how to I...

In class, we have been introduced to the supremum and infimum concepts and shown them on graphs, but I am wondering how to go about deriving them, and determining if they are part of the set, without actually having to graph them- especially for more complicated sets.

Thank you! This was my first attempt at an induction proof, so I wasn't too sure. Oh! I see the x2 now, thanks :)

Homework Statement Let a(1)=a(2)=5 and a(n+1)=a(n)+6a(n-1), n≥2 Use induction to prove that a(n)=(3^n)-(-2)^n for n≥1 Homework Equations Not applicable The Attempt at a Solution I have check that a(3) = 5+6·5 = 35 = 3^3-(-2)^3 so it holds for n = 3. The cases n = 1 and n = 2...