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Limiting Ratio (Posted on 2011-04-22) Difficulty: 4 of 5
F(n) is a function defined as:

F(n) = Σj=1 to n j6/2j

Evaluate this limit:

Limit F(n)
n → ∞

See The Solution Submitted by K Sengupta    
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easy/hard | Comment 1 of 3
It's easy to press a few buttons to come up with the strange looking result of 9366.  With n=57 this is accurate to at least 6 decimal places.

It's hard to derive this result analytically.  In fact, I'd assume there is a formula for any a>0 and b>1 for the sum of j^a/2^b.

  Posted by Jer on 2011-04-22 14:40:04
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