Given that
k=∞ 1 A*B-C*D
Σ ------------------ = -------
k=0 (3k+1)(3k+2)(3k+3) E
where A, B, C, D and E are, in some order, the number π (pi), the square root of an integer, the natural logarithm of an integer, and two integers, find their values.
(In reply to
re(4): confirm Charlie by pcbouhid)
Nothing rude.
Your expression to be summed 1/((3k+1)(3k+2)(3k+3)) = (3k)!/(3K+3)! is the reciprocal of a case of a Pochhammer function (nk+n)!/(nk)!which can be summed analytically giving a variety of interesting expressions of which yours is the case n = 3.
There are probably more elegant methods for solving the problem set by finding a suitable series for pi.
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Posted by goFish
on 2005-11-12 12:34:39 |
re(5): confirm Charlie
