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From: hopp@nbs-amrf.UUCP (Ted Hopp)
Newsgroups: net.math
Subject: Re: Ashby's solution to 1+11+...n 1's seems to be in error
Message-ID: <430@nbs-amrf.UUCP>
Date: Sun, 17-Feb-85 15:25:58 EST
Article-I.D.: nbs-amrf.430
Posted: Sun Feb 17 15:25:58 1985
Date-Received: Wed, 20-Feb-85 09:26:49 EST
References: <595@decwrl.UUCP>
Organization: National Bureau of Standards
Lines: 24

From: osman@sprite.DEC (Eric Osman, dtn 283-7484)
> Subject: Ashby's solution is wrong (to 1+11+111 . . .+ n 1's)

>  > |      Solution to  Sn = 1 + 11 + 111 + ... + 11...11                     |
>  > |                                             |<--->|                     |
>  > |                                              n 1's                      |
>  > |      is easily obtained by re-writing as                                |
>  > |                                                                         |
>  > |      (1)  Sn = (10^1 - 1)/9 + (10^2 - 1)/9 + ... + (10^n - 1)/9         |
>  > |                                                                         |
>  > |      re-arranging terms gives                                           |
>  > |                                                                         |
>  > |      (2)  Sn = 10*(10^n -1)/81  -  n/9                                  |
>  > |                                                                         |
>  > ===========================================================================
 
> There's something wrong with this solution !  s4 = 1+11+111+1111 = 1234.
> Let's  check: s4 = 10*(10^4-1)/81 - 4/9 = 10*9999/81 - 4/9 = 1234 + 16/81 -
> 4/9 DOES NOT EQUAL 1234 !!  [(4/9)^2 = 16/81 but so what]

Check your math.  10*9999/81 = 1234 + 36/81, not 1234 + 16/81.
-- 

Ted Hopp	{seismo,umcp-cs}!nbs-amrf!hopp