All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 An extended harmony (Posted on 2011-11-01)
How many members of the harmonic series 1+1/2+1/3+1/4+ …+1/n are needed to add up close to 10 , without going over it?

 No Solution Yet Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer verification | Comment 3 of 5 |
(In reply to A lower bound and a stab at a solution by Jer)

Indeed, the 12367th term is 0.0000808603541683512573785073178620522357887927549122665..., which causes the total to pass 10:

`            thru term    total              12365       9.9998812810285453761196033775747563846278551079819424280... 12366       9.9999621479216393434493785676119551554510800796785298451... 12367       10.000043008275807694706757074929817207686868872433442111... `

But, of course, after 12365 terms I'd still think that the total of over 9.99988 is near 10, though not as near as possible.

Term 7501, which is 0.000133315557925609918677509665377949606719..., is the one that brings the sum nearer to 10 than to 9: 9.50007394516904546697686643134742082130442987....

5   point 15
10   for I=1 to 100000
15       Pprev=Prev:Prev=T
20       T=T+1/I
25       if T>=9.5 and Prev<9.5 then print I:print 1/I:print Prev:print T
30       if T>=10 then print I:print 1/I:print Pprev:print Prev:print T:cancel for:goto 1000
100   next
1000   end

Edited on November 1, 2011, 12:34 pm
 Posted by Charlie on 2011-11-01 12:34:22

 Search: Search body:
Forums (0)