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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Progress? | Comment 11 of 15 |
(In reply to Progress? by dopey915)

Where n is the number of terms, the denominator is the average of the first 2^n powers of 3 divided by the average of the first 2^(n-1) powers of 3.

D(1) = ((3^0 + 3^1)/2) / 3^0 = 2

D(2) = ((3^0 + 3^1 + 3^2 + 3^3)/4) / ((3^0 +3^1)/2) = 5

D(3) = ((3^0 + 3^1 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6 + 3^7)/8) / ((3^0 + 3^1 + 3^2 + 3^3)/4) = 41

etc.


  Posted by MindRod on 2005-12-22 10:35:51
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