Abstract
We prove a combinatorial identity containing k-order differences of sequences, as well as binomial coefficients. The Euler summation operation implies the calculation of all order differences of terms of the initial series. The regularity of the summing function means the coincidence with the “ordinary” sum of the series, provided that this sum exists. The proved combinatorial identity allows one to easily prove the regularity of the Euler summation operation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.