Geodesic
The Euler summation of numerical series
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2020), pp. 76-82

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A combinatorial equality was proved, which involves k-order differences and binomial coefficients as well. The Euler's summing of a sequence connects with calculation of all differences. Regularity of summing function means the coincidence with “ordinary” sum, if the last exists. As a consequence of proving combinatorial equality the simple proof of regularity Euler's summing was given.
Keywords: summing of seriesies, Euler's summing, regularity of summing functions. 
@article{IVM_2020_7_a7,
     author = {N. I. Dubrovin},
     title = {The {Euler} summation of numerical series},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {76--82},
     publisher = {mathdoc},
     number = {7},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_7_a7/}
}
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N. I. Dubrovin. The Euler summation of numerical series. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2020), pp. 76-82. http://geodesic.mathdoc.fr/item/IVM_2020_7_a7/