Geodesic
A simple proof of the inequality $ e 3 $
Matematičeskoe obrazovanie, no. 2 (2023), pp. 17-19 
N. V. Ilyushechkin. A simple proof of the inequality $ e < 3 $. Matematičeskoe obrazovanie, no. 2 (2023), pp. 17-19. http://geodesic.mathdoc.fr/item/MO_2023_2_a3/
@article{MO_2023_2_a3,
     author = {N. V. Ilyushechkin},
     title = {A simple proof of the inequality $ e < 3 $},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {17--19},
     year = {2023},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2023_2_a3/}
}
TY  - JOUR
AU  - N. V. Ilyushechkin
TI  - A simple proof of the inequality $ e < 3 $
JO  - Matematičeskoe obrazovanie
PY  - 2023
SP  - 17
EP  - 19
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MO_2023_2_a3/
LA  - ru
ID  - MO_2023_2_a3
ER  - 
%0 Journal Article
%A N. V. Ilyushechkin
%T A simple proof of the inequality $ e < 3 $
%J Matematičeskoe obrazovanie
%D 2023
%P 17-19
%N 2
%U http://geodesic.mathdoc.fr/item/MO_2023_2_a3/
%G ru
%F MO_2023_2_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

Into a sequence that has its limit number $ e $, a simple additional factor is introduced, which tends to $1$. This modification allows us to prove inequality $e < 3$.

[1] E. S. Kochetkov, E. S. Kochetkova, Algebra i elementarnye funktsii. Uchebnoe posobie dlya uchaschikhsya 9 klassa srednei shkoly., Prosveschenie, M., 1969

[2] S. M. Nikolskii, M. K. Potapov, N. N. Reshetnikov, A. V. Shevkin, Algebra i nachala matematicheskogo analiza. 10 klass: uchebnik dlya obscheobrazovatelnykh uchrezhdenii: bazovyi i profilnyi urovni., Prosveschenie, M., 2009

[3] G. M. Fikhtengolts, Kurs differentsialnogo i integralnogo ischisleniya. Tom 1., Nauka, M., 1969

[4] G. P. Tolstov, Elementy matematicheskogo analiza. Tom 1., Nauka, M., 1974 | MR

[5] L. D. Kudryavtsev, Kurs matematicheskogo analiza. Tom 1., Vysshaya shkola, M., 1981 | MR

[6] N. S. Piskunov, Differentsialnoe i integralnoe ischisleniya. Tom 1., Mifril, Glavnaya redaktsiya fiziko-matematicheskoi literatury, SPb., 1996

[7] L. I. Kamynin, Kurs matematicheskogo analiza. Tom 1., Izdatelstvo Moskovskogo universiteta, M., 2001

[8] V. A. Ilin, E. G. Poznyak, Osnovy matematicheskogo analiza. Chast 1., Fizmatlit, M., 2005 | MR

[9] V. A. Zorich, Matematicheskii analiz. Chast 1., MTsNMO, M., 2007 | MR