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A185393 Decimal expansion of e/(e-1) = 1 + 1/e + 1/e^2 + ... 16
1, 5, 8, 1, 9, 7, 6, 7, 0, 6, 8, 6, 9, 3, 2, 6, 4, 2, 4, 3, 8, 5, 0, 0, 2, 0, 0, 5, 1, 0, 9, 0, 1, 1, 5, 5, 8, 5, 4, 6, 8, 6, 9, 3, 0, 1, 0, 7, 5, 3, 9, 6, 1, 3, 6, 2, 6, 6, 7, 8, 7, 0, 5, 9, 6, 4, 8, 0, 4, 3, 8, 1, 7, 3, 9, 1, 6, 6, 9, 7, 4, 3, 2, 8, 7, 2, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année, MP, Dunod, 1997, Exercice 3.3.29.a) pp. 286 and 307.
LINKS
Wikipedia, Tannery's theorem.
FORMULA
Equals Sum_{n>=0} 1/exp(n). - Vaclav Kotesovec, Jan 30 2015
From Vaclav Kotesovec, Oct 13 2018: (Start)
Equals 1 - LambertW(exp(1/(1 - exp(1))) / (1 - exp(1))).
Equals -LambertW(-1, exp(1/(1 - exp(1))) / (1 - exp(1))).
(End)
Equals Sum_{k>=0} (-1)^k*B(k)/k!, where B(k) is the k-th Bernoulli number. - Amiram Eldar, May 08 2021
Equals Integral_{x=0..oo} exp(-floor(x)) dx (Monier). - Bernard Schott, May 08 2022
Equals lim_{n->oo} Sum_{k=1..n} (k/n)^n (via Tannery's theorem). - Stoyan Apostolov, May 24 2022
EXAMPLE
1.58197670686932642438500200510901155854686930107539613626678705964804...
MATHEMATICA
RealDigits[E/(E - 1), 10, 100][[1]] (* G. C. Greubel, Jun 29 2017 *)
PROG
(PARI) exp(1)/(exp(1)-1)
(Python)
from sympy import E
print(list(map(int, str((E/(E-1)).n(88))[:-1].replace(".", "")))) # Michael S. Branicky, May 25 2022
CROSSREFS
Sequence in context: A122998 A227158 A098881 * A073333 A316229 A235936
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

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Last modified June 24 12:27 EDT 2024. Contains 373677 sequences. (Running on oeis4.)