Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site decwrl.UUCP Path: utzoo!watmath!clyde!bonnie!akgua!sdcsvax!dcdwest!ittvax!decvax!decwrl!dec-rhea!dec-sprite!osman From: osman@sprite.DEC (Eric Osman, dtn 283-7484) Newsgroups: net.math Subject: Ashby's solution to 1+11+...n 1's seems to be in error Message-ID: <595@decwrl.UUCP> Date: Fri, 15-Feb-85 12:45:39 EST Article-I.D.: decwrl.595 Posted: Fri Feb 15 12:45:39 1985 Date-Received: Sun, 17-Feb-85 05:57:50 EST Sender: daemon@decwrl.UUCP Organization: DEC Engineering Network Lines: 44 From: RHEA::DECWRL::"decvax!MAILER-DAEMON" 15-FEB-1985 12:12 To: decwrl!dec-rhea!dec-sprite!osman Subj: Returned mail: User unknown Received: from DECWRL by DEC-RHEA with SMTP; Fri, 15 Feb 85 09:14-PST Received: by decwrl.ARPA (4.22.01/4.7.34) id AA15361; Fri, 15 Feb 85 09:12:57 pst Received: by decvax.UUCP (4.12/1.0) id AA09323; Fri, 15 Feb 85 11:52:25 est Date: Friday, 15 Feb 1985 05:58:31-PST Return-Path: Message-Id: <8502151652.AA09323@decvax.UUCP> ----- Transcript of session follows ----- 550 net.math... User unknown ----- Unsent message follows ----- Received: by decvax.UUCP (4.12/1.0) id AA09321; Fri, 15 Feb 85 11:52:25 est Received: from DEC-RHEA.ARPA by decwrl.ARPA (4.22.01/4.7.34) id AA13235; Fri, 15 Feb 85 06:05:58 pst Message-Id: <8502151405.AA13235@decwrl.ARPA> Date: Friday, 15 Feb 1985 05:58:31-PST From: decwrl!dec-rhea!dec-sprite!osman (Eric Osman, dtn 283-7484) To: harpo!whuxlm!whuxl!houxm!ihnp4!inuxc!pur-ee!uiucscsp!ashby@decvax, decwrl!dec-rhea!dec-sprite!net.math 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]