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Factorial Ratio Sum Puzzle (Posted on 2015-08-04) Difficulty: 3 of 5
Define:
A(k) = k! + (k+1)! + (k+2)!, and:

B(n) = Σk=1 to n (k+2)/A(k)

Evaluate:

Limit B(n)
n → ∞

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution: It quickly converges | Comment 2 of 3 |
2 .458333333333333
3 .491666666666667
4 .498611111111111
5 .499801587301587
6 .499975198412698
7 .499997244268078
8 .499999724426808
9 .499999974947892
10 .499999997912324
11 .49999999983941
12 .499999999988529
13 .499999999999235
14 .499999999999952
15 .499999999999997
16 .5
17 .5
18 .5
19 .5
20 .5
21 .5
22 .5
23 .5
24 .5
25 .5
26 .5
27 .5
28 .5
29 .5
30 .5
31 .5
32 .5
33 .5
34 .5
35 .5
36 .5
37 .5

from the first few lines out of

DefDbl A-Z
Dim crlf$


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

 k = 1: f1 = 1: f2 = 2: f3 = 6
 b = 3 / (f1 + f2 + f3)
 For n = 2 To 100
   f1 = f2: f2 = f3: f3 = f3 * (n + 2)
   b = b + (n + 2) / (f1 + f2 + f3)
   Text1.Text = Text1.Text & n & Str(b) & crlf
 Next
 
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


  Posted by Charlie on 2015-08-04 09:14:25
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