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From: Virgil on 25 Sep 2006 16:04
In article <1159213528.903733.67400(a)e3g2000cwe.googlegroups.com>,
Han.deBruijn(a)DTO.TUDelft.NL wrote:

> Virgil wrote:
>
> > Def: 0.333... = lim_{n -> oo} Sum_{k = 1..n} 1/3^n
>
> Oh?
>
> 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289 > 0.333
>
> Han de Bruijn

My typo. My (1/3)^n should have been (3/10)^n.

But your typo says
"1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289"
Which is off by a factor of almost 10.
From: Gerard Schildberger on 25 Sep 2006 16:43
| Virgil wrote:
|> Han.deBruijn wrote:
|>> Virgil wrote:
|> > Def: 0.333... = lim_{n -> oo} Sum_{k = 1..n} 1/3^n

|> Oh?
|>
|> 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289 > 0.333
|>
|> Han de Bruijn

| My typo. My (1/3)^n should have been (3/10)^n.
|
| But your typo says
| "1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289"
| Which is off by a factor of almost 10.

for (3/10)^n, the sum for 100 terms is around 0.42857142857+
________________________________________________________Gerard S.



From: Han.deBruijn on 25 Sep 2006 16:55
Virgil schreef:

> In article <1159213528.903733.67400(a)e3g2000cwe.googlegroups.com>,
> Han.deBruijn(a)DTO.TUDelft.NL wrote:
>
> > Virgil wrote:
> >
> > > Def: 0.333... = lim_{n -> oo} Sum_{k = 1..n} 1/3^n
> >
> > Oh?
> >
> > 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289 > 0.333
> >
> > Han de Bruijn
>
> My typo. My (1/3)^n should have been (3/10)^n.
>
> But your typo says
> "1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289"
> Which is off by a factor of almost 10.

Yeah. Ooops. I meant 0.4993141289 here. But the limit is 0.5,
of course.

Han de Bruijn

From: Han.deBruijn on 25 Sep 2006 16:58
Gerard Schildberger schreef:

> | Virgil wrote:
> |> Han.deBruijn wrote:
> |>> Virgil wrote:
> |> > Def: 0.333... = lim_{n -> oo} Sum_{k = 1..n} 1/3^n
>
> |> Oh?
> |>
> |> 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289 > 0.333
> |>
> |> Han de Bruijn
>
> | My typo. My (1/3)^n should have been (3/10)^n.
> |
> | But your typo says
> | "1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289"
> | Which is off by a factor of almost 10.
>
> for (3/10)^n, the sum for 100 terms is around 0.42857142857+
> ________________________________________________________Gerard S.

And the sum of the geometric series as a whole is 1/2 . Heheh ...

Han de Bruijn

From: Virgil on 25 Sep 2006 17:03
In article <2OudnWd259sao4XYnZ2dnUVZ_u-dnZ2d(a)onvoy.com>,
"Gerard Schildberger" <Gerard46(a)rrt.net> wrote:

> | Virgil wrote:
> |> Han.deBruijn wrote:
> |>> Virgil wrote:
> |> > Def: 0.333... = lim_{n -> oo} Sum_{k = 1..n} 1/3^n
>
> |> Oh?
> |>
> |> 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289 > 0.333
> |>
> |> Han de Bruijn
>
> | My typo. My (1/3)^n should have been (3/10)^n.
> |
> | But your typo says
> | "1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + ... > 4.993141289"
> | Which is off by a factor of almost 10.
>
> for (3/10)^n, the sum for 100 terms is around 0.42857142857+
> ________________________________________________________Gerard S.

I'm really being sloppy today, (3/10)^n should be 3/ (10^n).
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