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.
Hello fellow science fans,
We here at Isaac’s Science Blog are very pleased to announce our first guest post done by no other than Matthew Hannah! Matthew is a 4th-year mathematics student at
the University of California, Riverside. His current research interests include
Functional Analysis and Representation Theory. You can read his post about the Convergence of Infinite Sums here.
“What is a more optimal fuel than gasoline?”
While gasoline is the most widespread vehicle fuel in the world, recent advances in science and technology have created competitors. One in particular comes in the form of Methanol Fuel. Methanol fuel is synthesized from carbon dioxide and hydrogen burns cleaner and is cheaper to produce sustainably than ethanol. Since it does not produce a thick cloud of smoke upon use, it is often used in racing applications. Although methanol is less toxic than petroleum, there exist very few methanol refueling stations, it is commonly found in a mixture with other fuels.
Image credit https://toxtown.nlm.nih.gov