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Not too much (Posted on 2015-02-20) Difficulty: 2 of 5
What is the sum of the reciprocals of all the nonzero
triangular numbers?

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts re(2): Is this valid? no ! - partial spoiler | Comment 5 of 8 |
(In reply to re: Is this valid? no ! - partial spoiler by Ady TZIDON)

successively better approximations by adding terms:


(total shown after every 10,000 terms)

1.999800019998
1.99990000499975
1.99993333555549
1.99995000124998
1.9999600008
1.99996666722223
1.99997142897961
1.99997500031252
1.99997777802472
1.99998000020002
1.99998181834714
1.99998333347225
1.99998461550298
1.99998571438777
1.99998666675558
1.99998750007814
1.99998823536333
1.99998888895063
1.99998947373963
1.99999000005001
1.99999047623586
1.99999090913226
1.99999130438567
1.99999166670143
1.99999200003205
1.99999230772194
1.99999259262011
1.99999285716846
1.99999310347215
1.99999333335565
1.999993548408
1.99999375001962
1.99999393941239
1.99999411766443
1.99999428573069
1.99999444445995
1.99999459460928
1.99999473685603
1.99999487180809
1.99999500001257
1.99999512196319
1.99999523810665
1.9999953488481
1.99999545455586
1.99999555556551
1.99999565218344
1.99999574468998
1.99999583334209
1.99999591837575
1.99999600000808
1.99999607843914
1.99999615385363
1.9999962264223
1.99999629630324
1.99999636364306
1.99999642857789
1.99999649123431
1.99999655173017
1.99999661017532
1.9999966666723
1.99999672131693
1.99999677419883
1.99999682540194
1.99999687500496
1.99999692308174
1.99999696970165
1.99999701492991
1.99999705882794
1.99999710145356
1.99999714286131
1.99999718310264
1.99999722222617
1.99999726027781
1.99999729730104
1.99999733333698
1.99999736842461
1.99999740260087
1.99999743590081
1.99999746835773
1.99999750000322
1.99999753086734
1.99999756097868
1.99999759036444
1.99999761905055
1.99999764706168
1.9999976744214
1.99999770115216
1.9999977272754
1.99999775281161
1.99999777778034
1.99999780220031
1.99999782608941
1.99999784946477
1.99999787234278
1.99999789473915
1.99999791666893
1.99999793814655
1.99999795918585
1.99999797980011
1.99999800000209

DefDbl A-Z
Dim crlf$
Function mform$(x, t$)
  a$ = Format$(x, t$)
  If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
  mform$ = a$
End Function

Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True

 For i = 1 To 1000000
  adder = adder + 1
  tri = tri + adder
  tot = tot + 1 / tri
  If i Mod 10000 = 0 Then Text1.Text = Text1.Text & tot & crlf
 Next


End Sub

  Posted by Charlie on 2015-02-20 15:16:45
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