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Evaluate this sum (Posted on 2005-12-21) Difficulty: 4 of 5
Evaluate this sum in terms of n (the number of terms):
        1      2       4        8          16         
   S = --- + ----- + ----- + ------- + ---------- + ..... 
        2      5       41     3,281    21,523,361              

See The Solution Submitted by pcbouhid    
Rating: 4.3333 (3 votes)

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Some Thoughts Partial Solution | Comment 3 of 14 |
 
I get the following:
  S_n = 1 - (1/Q_n)
where
  Q_n = 2                           if n = 0
      = Q_(n-1)*(2^n*Q_(n-1) + 1)   if n > 0
I'm still working on a closed form.
 

  Posted by Bractals on 2005-12-21 15:20:41
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