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%I #16 Nov 19 2020 04:45:52
%S 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,
%T 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,
%U 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
%N Decimal expansion of Sum_{n>=1} -(-1)^n*(e - (1 + n^(-1))^n).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlternatingSeries.html">Alternating Series</a>.
%F Equals Sum_{k>=1} f(2*k) - f(2*k-1), where f(k) = (1 + 1/k)^k. - _Amiram Eldar_, Nov 19 2020
%e 0.44562240319683333408852796749015199821221222217046014366347362057...
%p evalf(Sum(-(-1)^n*(exp(1) - (1 + n^(-1))^n), n=1..infinity), 120); # _Vaclav Kotesovec_, Mar 01 2016
%t 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 *)
%o (PARI) sumalt(n=1, -(-1)^n*(exp(1) - (1 + n^(-1))^n)) \\ _Michel Marcus_, Nov 19 2020
%Y Cf. A001113.
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_, Jan 03 2006