A114884 Decimal expansion of Sum_{n>=1} -(-1)^n*(e - (1 + n^(-1))^n).

4, 4, 5, 6, 2, 2, 4, 0, 3, 1, 9, 6, 8, 3, 3, 3, 3, 4, 0, 8, 8, 5, 2, 7, 9, 6, 7, 4, 9, 0, 1, 5, 1, 9, 9, 8, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 7, 0, 4, 6, 0, 1, 4, 3, 6, 6, 3, 4, 7, 3, 6, 2, 0, 5, 7, 1, 4, 3, 5, 2, 9, 4, 7, 0, 9, 8, 2, 9, 4, 8, 4, 0, 7, 1, 3, 3, 6, 9, 0, 1, 3, 2, 9, 7, 8, 5, 2, 4, 9, 1, 5, 0

Offset

0,1

Links

Table of n, a(n) for n=0..101.

Eric Weisstein's World of Mathematics, Alternating Series.

Formula

Equals Sum_{k>=1} f(2*k) - f(2*k-1), where f(k) = (1 + 1/k)^k. - Amiram Eldar, Nov 19 2020

Example

0.44562240319683333408852796749015199821221222217046014366347362057...

Maple

evalf(Sum(-(-1)^n*(exp(1) - (1 + n^(-1))^n), n=1..infinity), 120); # Vaclav Kotesovec, Mar 01 2016

Mathematica

RealDigits[ Chop[ NSum[ -(-1)^n*(E - (1 + n^(-1))^n), {n, Infinity}, NSumTerms -> 2^8, NSumExtraTerms -> 2^6, WorkingPrecision -> 2^8]]][[1]] (* Robert G. Wilson v, Jan 05 2006 *)

Prog

(PARI) sumalt(n=1, -(-1)^n*(exp(1) - (1 + n^(-1))^n)) \\ Michel Marcus, Nov 19 2020

Crossrefs

Cf. A001113.

Sequence in context: A082968 A136013 A232172 * A132704 A202151 A368552

Adjacent sequences: A114881 A114882 A114883 * A114885 A114886 A114887

Keyword

nonn,cons

Author

Eric W. Weisstein, Jan 03 2006

Status

approved