Cut the Cards
06-23-2021, 12:08 AM
Post: #19
 Albert Chan Senior Member Posts: 1,848 Joined: Jul 2018
RE: Cut the Cards
An integral, from a very old (2006) thread: So your HP can INTEGRATE ...
I revived the old thread recently, for an integral that HP71B failed, see HP71B IBOUND fooled

Code:
            / Inf             |     FRAC(x)      I7 =   |     -------  .dx             |       x²            / 1

I put the solution here because integral is closely related to harmonic number

I7 = ∫((x-1)/x^2, x=1..2) + ∫((x-2)/x^2, x=2..3) + ∫((x-3)/x^2, x=3..4) + ...
﻿ ﻿ ﻿ ﻿ =﻿ (ln(2) - ln(1) - 1/2)﻿ ﻿ ﻿ ﻿ + (ln(3) - ln(2) - 1/3) ﻿ ﻿ + (ln(4) - ln(3) - 1/4) ﻿ ﻿ ﻿ + ...

$$I_7 - 1 = \displaystyle \lim_{n \to ∞} (\,\ln(n) - H_n\,) = - \gamma$$

$$I_7 = 1 - \gamma ≈ 0.422784$$
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 Messages In This Thread Cut the Cards - David Hayden - 07-30-2020, 08:00 PM RE: Cut the Cards - Albert Chan - 07-30-2020, 08:58 PM RE: Cut the Cards - Albert Chan - 08-21-2020, 11:00 PM RE: Cut the Cards - Jim Horn - 07-30-2020, 09:49 PM RE: Cut the Cards - John Keith - 07-31-2020, 12:24 AM RE: Cut the Cards - Gerson W. Barbosa - 08-24-2020, 01:57 PM RE: Cut the Cards - Albert Chan - 08-25-2020, 06:14 PM RE: Cut the Cards - Albert Chan - 07-30-2020, 10:21 PM RE: Cut the Cards - pinkman - 08-24-2020, 09:49 PM RE: Cut the Cards - Gerson W. Barbosa - 08-25-2020, 11:41 PM RE: Cut the Cards - Albert Chan - 08-26-2020, 03:06 AM RE: Cut the Cards - Gerson W. Barbosa - 08-26-2020, 08:23 AM RE: Cut the Cards - Albert Chan - 08-26-2020, 02:13 PM RE: Cut the Cards - Gerson W. Barbosa - 08-26-2020, 06:13 PM RE: Cut the Cards - Gerson W. Barbosa - 08-27-2020, 10:07 PM RE: Cut the Cards - Albert Chan - 08-28-2020, 09:26 PM RE: Cut the Cards - Albert Chan - 08-29-2020, 04:02 PM RE: Cut the Cards - Gerson W. Barbosa - 08-28-2020, 11:39 PM RE: Cut the Cards - Albert Chan - 06-23-2021 12:08 AM

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