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Old 12-08-2005, 09:00 PM
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Default Re: Infinite multiplication

Cool... thanks. [img]/images/graemlins/smile.gif[/img]

I wrote a perl script (before I saw your anwer), and it didn't seem to converge. Here is the output:

<font class="small">Code:</font><hr /><pre>$i = 2 $prec = 2 0.98
$i = 3 $prec = 5 0.97804
$i = 4 $prec = 9 0.977844392
$i = 5 $prec = 14 0.97782483511216
$i = 6 $prec = 20 0.97782287946248977568
$i = 7 $prec = 27 0.977822683897913883182044864
$i = 8 $prec = 35 0.97782266434146020522376720035910272
$i = 9 $prec = 44 0.97782266238581487654084678991156831928179456
$i = 10 $prec = 54 0.977822662190250344063683814603398961299480896143 641088
$i = 11 $prec = 65 0.977822662170693890819878807722125285007412916917 65147007712717824
$i = 12 $prec = 77 0.977822662168738245495537419940485527391968666347 63664424329187529984574564352
$i = 13 $prec = 90 0.977822662168542680963103672291386419907980569242 15825051002234797099708726846003
$i = 14 $prec = 104 0.977822662168523124509860301437767157834534741513 76009089863750480598688682150061
$i = 15 $prec = 119 0.977822662168521168864535964391518138113931865979 44442182915447728580508954649099
$i = 16 $prec = 135 0.977822662168520973300003530687284365206738987675 81679904278128139692072371559554
$i = 17 $prec = 152 0.977822662168520953743550287316864899206668373930 12949490800152788058474285996991
$i = 18 $prec = 170 0.977822662168520951787904962979822991719567799296 39969649466478002032575304396685
$i = 19 $prec = 189 0.977822662168520951592340430546118801361986806700 43509815075122016104581374503390
$i = 20 $prec = 209 0.977822662168520951572783977302748382330139998089 51272212351148402703711178201887
$i = 21 $prec = 230 0.977822662168520951570828331978411340426994430134 90722535885120403085808633777185
$i = 22 $prec = 252 0.977822662168520951570632767445977636236680264468 51154309076580514483110489270008
$i = 23 $prec = 275 0.977822662168520951570613210992734265817648851813 16262353804107153954173466183826
$i = 24 $prec = 299 0.977822662168520951570611255347409928775745710586 74063806950943624183810833659119
$i = 25 $prec = 324 0.977822662168520951570611059782877495071555396464 48956858752368109269599098846357
$i = 26 $prec = 350 0.977822662168520951570611040226424251701136365052 26837292997377966158806169867220
$i = 27 $prec = 377 0.977822662168520951570611038270778927364094461911 04629247712527625931533159413546
$i = 28 $prec = 405 0.977822662168520951570611038075214394930390271596 92408482296949078649643921192620
$i = 29 $prec = 434 0.977822662168520951570611038055657941687019852565 51186406146520288788863377998772
$i = 30 $prec = 464 0.977822662168520951570611038053702296362682810662 37064198535388700451459407485669
$i = 31 $prec = 495 0.977822662168520951570611038053506731830249106472 05651977774314654524205751272422
$i = 32 $prec = 527 0.977822662168520951570611038053487175377005736053 02510755698207641060545253059478
$i = 33 $prec = 560 0.977822662168520951570611038053485219731681399011 12196633490596943625469851912267
$i = 34 $prec = 594 0.977822662168520951570611038053485024167148965306 93165221269835873921075218284287
$i = 35 $prec = 629 0.977822662168520951570611038053485004610695721936 51262080047759766951026883986356
$i = 36 $prec = 665 0.977822662168520951570611038053485002655050397599 47071765925552156254025961847212
$i = 37 $prec = 702 0.977822662168520951570611038053485002459485865165 76652734513331395184325908746204
$i = 38 $prec = 740 0.977822662168520951570611038053485002439929411922 39610831372109319077355903827232
$i = 39 $prec = 779 0.977822662168520951570611038053485002437973766598 05906641057987111466658903339246
</pre><hr />

I had to stop at 39 because my "BigFloat" could only hold 819 decimal points.

By the way, I used the following forumla to calcluate the result:

$newresult = $oldresult * (((10^i)-2)/(10^i)) [i = 2 .. 39]
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