On 18 Mar, 15:06, "Salva" <salvas...@[EMAIL PROTECTED]
> wrote:
> Hello,
> can you detect a pattern in the decimals sequence of this :
>
> (for n=3Dinfinite) =A0Sn=3D1/((10^n)-1) =A0?
>
> If you find it difficult subtract 0.022222... from the previous sum.
>
> Salvatore
My guess is that you mean
Sum_{n=3D1 to inf} 1/((10^n)-1)
=3D 1/9 + 1/99 + 1/999 + 1/9999 + ...
which is roughly
0.122324243426244526264428344628264449244828266430364628484432246748
The first 46 decimal digits of this represent the number of divisors
of positive integers (e.g. the twelth digit is 6 and twelve has six
divisors, namely 1, 2, 3, 4, 6, and 12). There is a problem later:
for example 48 has ten divisors, namely 1, 2, 3, 4, 6, 8, 12, 16, 24,
and 48, and there is no ten digit in decimal.
I am not sure how 0.022222... helps.
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