#### Title

Evaluating Limits of Series

#### School Name

Governor's School for Science and Mathematics

#### Grade Level

12th Grade

#### Presentation Topic

Mathematics

#### Presentation Type

Mentored

#### Abstract

Mathematicians are interested in classifying numbers and distinguishing between different sets of them. Work in pure mathematics has been used in such diverse fields as encryption, astrophysics, and phylogenetics. Riemann sum are a method of approximating an integral with a summation, and the reverse can be done to approximate a summation with an integral. The squeeze theorem states that if an upper bound and a lower bound of a function converge to the same limit, the function must converge to that limit. Using these techniques, the limiting value of a series of exponential terms can be found in a closed form. Similar methods might be applicable to the Euler-Mascheroni constant to determine whether it is rational or irrational.

#### Recommended Citation

Ravan, Brennan, "Evaluating Limits of Series" (2018). *South Carolina Junior Academy of Science*. 64.

https://scholarexchange.furman.edu/scjas/2018/all/64

#### Location

Neville 206

#### Start Date

4-14-2018 11:15 AM

#### Presentation Format

Oral and Written

Evaluating Limits of Series

Neville 206

Mathematicians are interested in classifying numbers and distinguishing between different sets of them. Work in pure mathematics has been used in such diverse fields as encryption, astrophysics, and phylogenetics. Riemann sum are a method of approximating an integral with a summation, and the reverse can be done to approximate a summation with an integral. The squeeze theorem states that if an upper bound and a lower bound of a function converge to the same limit, the function must converge to that limit. Using these techniques, the limiting value of a series of exponential terms can be found in a closed form. Similar methods might be applicable to the Euler-Mascheroni constant to determine whether it is rational or irrational.