<se16@[EMAIL PROTECTED]
> wrote in message
news:83d872d4-c0d8-40a8-8761-fd781e68084d@[EMAIL PROTECTED]
18 Mar, 15:06, "Salva" <salvas...@[EMAIL PROTECTED]
> wrote:
> Hello,
> can you detect a pattern in the decimals sequence of this :
>
> (for n=infinite) Sn=1/((10^n)-1) ?
>
> If you find it difficult subtract 0.022222... from the previous sum.
>
> Salvatore
My guess is that you mean
Sum_{n=1 to inf} 1/((10^n)-1)
= 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.
Hello,
sorry, when I posted I was in a hurry. Anyway you've understood what I
meant.
If the Nth decimal is 2 then N is a prime number; it works until 48 but it
is interesting anyway.
If we consider 1/9 + 1/99 we have 0.12121212 ..., a simmetry with periode
lenght 2, if we add 1/9 + 1/99 + 1/999 we have 0.122213122213122213...
periode lenght 6 , etc.
You can add as many fractions as you want, but it will be always a
recurring
decimals ( as long as N!);
can we still say that this number is an irrational number even though
there
is a simmetry ?
Can this way of representing primes be usefull by manipulating it ?
Sorry for swearing ...
Ciao
Salva
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