F(n) is a function defined as:

F(n) = Σ_{j=1 to n} j⁶/2^j

Evaluate this limit:

Limit F(n)
n → ∞

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