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Path: utzoo!watmath!clyde!bonnie!akgua!whuxlm!harpo!decvax!cca!ima!ISM780!ed
From: ed@ISM780.UUCP
Newsgroups: net.math
Subject: Re: Orphaned Response
Message-ID: <93@ISM780.UUCP>
Date: Sun, 17-Feb-85 00:23:52 EST
Article-I.D.: ISM780.93
Posted: Sun Feb 17 00:23:52 1985
Date-Received: Mon, 18-Feb-85 05:20:06 EST
Lines: 40
Nf-ID: #R:charm:-58600:ISM780:30200001:177600:838
Nf-From: ISM780!ed    Feb 14 10:08:00 1985

/* Written  5:20 am  Feb 13, 1985 by mam@charm in ISM780:net.math */

A netter asked:
1)	What is the sum  of
1 + 11 + 111 + ... {n ones} ?
2)	At what time between 4:00 and 5:00 do the hour and minute hands of
a clock form a right angle?

My (possible buggy) solutions:
1) This series contains:
n 1's
n-1 10's
n-2 100's
...
1 10^n.

**********************

Your representation is incorrect; e.g., if n=2, you are saying the sum has
2 1's, and 1 100.  Obviously, the last one should be "1 10^n-1".

Regardless, a far easier way to solve this problem is to realize that
each term t  in the sum can be expressed as:
	   i
	      i
	t = 10 - 1
	 i  ------
	      9

Then it is easily shown that

	   n
	  ---
	  \           n+1
	  /   t   = 10   - 10 - 9n
	  ---  i    --------------
	  i=1            81

Ed Lycklama
decvax!cca!ima!ism780!ed