AboutScotto Expertise Any kind of mathematics (calculus, analysis, game theory, linear approximation, finite differences, linear regression, linear programming, numerical analysis, probability, statistics, etc.).
I also have answered some questions in
Physics (mass, momentum, falling bodies),
Chemistry (charge, reactions, symbols, molecules), and
Biology.
Experience Experience in the area: I have tutored students in all areas of mathematics for over 20 years.
Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors.
Awards and Honors: I have passed Actuarial tests 100, 110, and 135.
Publications Maybe not a publication, but I have respond to well oveer 3000 questions on the PC.
That's around 2,000 in basic math and 1,000 in advanced math.
Education/Credentials I aquired well over 40 hours of upper division courses. This was well over the number that were required.
I graduated with honors in both my BS and MS degree from Oregon State University.
I was allowed to jump into a few junior level courses my sophomore year.
Awards and Honors I have been nominated as the expert of the month several times.
All of my scores right now are at least a 9.8 average (out of 10).
Past/Present Clients My past clients have been students at OSU, students at the college in South Seattle,
referals from a company, friends and aquantenances, people from my church, and people like you.
Question With the aid of anything (excel , computer code), how can I argue that the series 1+1/2+1/3+1/4+1/5 .... diverges.
Answer This series can be made into a function f(x)=int(1/a) on [a-1,a] for all a from 1 to ∞. The summation of the function from 1 to ∞ is therefore equal to the integral from 1 to ∞.
The function f(x)=1/2x is below this function for all x. Integrating this function gives ln(x)/2 to be evaluated from 1 to infinity.
The lower limit, ln(1), is 0, but ln(∞) is ∞.
Therefore, since the summation is greater than a the integral of this function and this function diverges, the summation diverges as well.
