A371936 -id:A371936 - cp's OEIS frontend

A206533 Decimal expansion of 1/(1-cos(1)).

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

Offset: 1

Seiichi Kirikami, Feb 11 2012

The value of the fractional limit of the numerators(A206531+2*A206532) and the denominators(A206532).

Abs(A206532/(1-cos(1)) - (A206531+2*A206532)) -> 0.

			2.17534264967002141077678675965606997584844...

E. W. Cheney, Introduction to Approximation Theory, McGraw-Hill, Inc., 1966.

Cf. A002939, A082108, A206531, A206532, A049470, A371936.

Mathematica
```
RealDigits[N[1/(1-Cos[1]), 150]][[1]]
```

1/(1 - cos(1)) \\ Stefano Spezia, Apr 21 2025

Equals 1/(1-A049470).
A206531/A206532+2 -> 1/(1-A049470).
Equals 1/A371936. - Hugo Pfoertner, Apr 21 2025

Incorrect a(86)=9 removed by Georg Fischer, Apr 04 2020

A371935 Decimal expansion of Sum_{k>=0} (-1)^k / ((k+1)(2k+1)!).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Apr 24 2024

			0.91939538826372056519812678511404679253...

Cf. A049470, A243596, A272795, A371936.

s = N[Sum[(-1)^k/((k + 1) (2 k + 1)!), {k, 0, Infinity}], 120]
First[RealDigits[s]]

2*(1 - cos(1)) \\ Stefano Spezia, Apr 21 2025

Equals 2*(1 - cos(1)) = 2 * A371936.
From Hugo Pfoertner, Apr 26 2024: (Start)
Equals A243596/Pi.
Equals A272795^2. (End)

cp's OEIS Frontend

A206533 Decimal expansion of 1/(1-cos(1)).

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A371935 Decimal expansion of Sum_{k>=0} (-1)^k / ((k+1)(2k+1)!).

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cp's OEIS Frontend

A206533 Decimal expansion of 1/(1-cos(1)).

Views

Author

Keywords

Comments

Examples

References

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A371935 Decimal expansion of Sum_{k>=0} (-1)^k / ((k+1)*(2*k+1)!).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Formula

A371935 Decimal expansion of Sum_{k>=0} (-1)^k / ((k+1)(2k+1)!).