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# (e-1)/(e+1)

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## Contents

## (e-1)/(e+1)

### Decimal expansion of (e-1)/(e+1)

The decimal expansion is

where is the hyperbolic tangent of . This gives the sequence of decimal digits (Cf. A160327)

- {4, 6, 2, 1, 1, 7, 1, 5, 7, 2, 6, 0, 0, 0, 9, 7, 5, 8, 5, 0, 2, 3, 1, 8, 4, 8, 3, 6, 4, 3, 6, 7, 2, 5, 4, 8, 7, 3, 0, 2, 8, 9, 2, 8, 0, 3, 3, 0, 1, 1, 3, 0, 3, 8, 5, 5, 2, 7, 3, 1, 8, 1, 5, 8, 3, 8, 0, 8, 0, 9, 0, 6, 1, 4, 0, 4, 0, 9, 2, 7, 8, 7, ...}

### Continued fraction for (e-1)/(e+1)

The continued fraction is

giving the sequence of partial quotients (Cf. A016825)

- {0, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, ...}

## (e+1)/(e-1)

### Decimal expansion of (e+1)/(e-1)

The decimal expansion is

where is the hyperbolic cotangent of . This gives the sequence of decimal digits (Cf. A??????)

- {2, 1, 6, 3, 9, 5, 3, 4, 1, 3, 7, 3, 8, 6, 5, 2, 8, 4, 8, 7, 7, 0, 0, 0, 4, 0, 1, 0, 2, 1, 8, 0, ...}

### Continued fraction for (e+1)/(e-1)

The continued fraction is

giving the sequence of partial quotients (Cf. A016825)

- {2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, ...}

which happens to be the number of electrons per filled orbital of the atom.

## See also