Geodesic
A simple proof of the inequality $ e 3 $
Matematičeskoe obrazovanie, Tome 106 (2023) no. 2, pp. 17-19

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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 $e 3$. 
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     author = {N. V. Ilyushechkin},
     title = {A simple proof of the inequality $ e < 3 $},
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N. V. Ilyushechkin. A simple proof of the inequality $ e < 3 $. Matematičeskoe obrazovanie, Tome 106 (2023) no. 2, pp. 17-19. http://geodesic.mathdoc.fr/item/MO_2023_106_2_a3/