Category: Guest Post
Welcome to the 3rd installment of Matt’s Math Mondays! I am pleased to introduce to you one of the most powerful and applicable ideas in math known as groups! I hope you all have as much fun reading it as I had writing it.
Hello! This 2nd post in Matt’s Math Mondays is concerns a problem in first order logic. I reckon many of you have not taken an in depth course so this might be a little bit difficult. However, there is without a doubt in my mind with some elbow grease, you will be to understand and appreciate the problem!
On Convergence of Infinite Sums
“What is so special about infinite sums coming to a specific value?”
We have all seen the classic sum.
Which is often represented as…
We, in our high school careers, have been taught that this sum is 2. This is
most often done so with an algebraic manipulation of both sides of the sum. We
haven’t been taught how to verify this sum. But how would we go about doing
The basic idea is that if I end my sum at nite point, my result will deviate
from the actual sum by some error (which we will call ε. This error is some
positive real number. To verify that this sum indeed approaches 2, it suffices
to show that for any error, there exists a nite point in the series in which the
difference between 2 and this point is less than the error AND all further points
will also be less than the error.