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Sick-quence (Posted on 2019-03-20) Difficulty: 3 of 5
1-(1/11)+(1/11*3/22)-(1/11*3/22*5/33)+.... = ?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution computer solution Comment 1 of 1
It's sqrt(11/13):

 tot = 1
 term = 1
 For i = 1 To 100
   term = -term * (2 * i - 1) / (11 * i)
   prev = tot
   tot = tot + term
   If tot = prev Then Exit For
   Text1.Text = Text1.Text & term & Str(tot) & crlf
 Next

finds  0.9198662110078

The simplest Wolfram Alpha identification of a closed form for this is sqrt(11/13). The next "simplest" is (4 - 17 pi + 48 pi^2)/(8 (-2 - 3 pi + 7 pi^2)) ~= 0.919866211007875643.

   5    point 13
  10    tot = 1
  20     term = 1
  30     For i = 1 To 200
  40       term = -term * (2 * i - 1) / (11 * i)
  50       prev = tot
  60       tot = tot + term
  70       If tot = prev Then cancel for: goto 100
  80       print Str(tot) 
  90     Next
 100     print sqrt(11/13) 
 110     open "sickqnce.txt" for output as #2
 120     print #2, tot:print #2,sqrt(11/13)
 130     close #2
     
verifies, to a greater precision

the total of the sequence:
 0.91986621100779984777921851970735512415316048347209214708907934 
and sqrt(11/13): 
 0.91986621100779984777921851970735512415316048347209214708907934 


  Posted by Charlie on 2019-03-20 11:13:28
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