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??
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.
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...