Abstract
The binomial coefficients are an almost endless source of formulas for the summation of series. A reference to the “Problems for Solution” pages of the American Mathematical Monthly or to an advanced collection of mathematical formulas will convince anyone who has not yet discovered this for himself. Some of these series summations can be derived with relative ease with the help of the binomial theorem or Pascal's triangle; many require a high degree of virtuosity in algebraic manipulation and, often, advanced methods of analysis. A number of them can be obtained simply by reasoning logically about the meaning of certain combinatorial expressions, with recourse to only a minimum of algebra or to none at all. These, naturally, have a special appeal of their own, and it is the purpose of this article to illustrate several such derivations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
