1-(1/11)+(1/11*3/22)-(1/11*3/22*5/33)+.... = ?
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
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Posted by Charlie
on 2019-03-20 11:13:28 |
computer solution