A282821 Decimal expansion of Sum_{k >= 0} (4/(4*k+1) - 3/(3*k+1) + 2/(2*k+1) - 1/(k+1)).

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

Offset: 1

Author

Bruno Berselli, Mar 03 2017

Keywords

• nonn
• cons

Comments

It is known that Sum_{k >= 0} Sum_{i = 1..h} (-1)^i*i/(i*k + 1) diverges for h = 3. This is the case h = 4, A016627 corresponds to the case h = 2.

Examples

			2.48171411447534970392757531472576785936281641070833471570388837547057328...
		

Crossrefs

Cf. A016627.

Programs

Mathematica

RealDigits[(3 - Sqrt[3]) Pi/6 + Log[32] - Log[27]/2, 10, 100][[1]]

Formula

Equals (3 - sqrt(3))*Pi/6 + log(32) - log(27)/2.