Re: Help: How to calculate quickly this sum 192,255,317....1218,1262?
- From: Anon <spamhole@xxxxxxxxxxxxxxxxx>
- Date: Sun, 26 Feb 2006 06:05:48 GMT
On 25 Feb 2006 03:50:28 -0800, "gnh888@xxxxxxxxx" <gnh888@xxxxxxxxx>
wrote:
Yes, this is a polynomial.
How is this polynomial going to help me to calculate the sum?
What is the name of such a series?
Any chance to explain how you calculate the sum?
Reference websites would be appreciated?
gnh888
Regarding "the polynomial", see the theory and example here:
http://mathworld.wolfram.com/FiniteDifference.html
Then, to find an equation for the sum, the second post by Kiuhnm
said this:
The polynomial is
p(x) = 128 + 129x/2 - x^2/2.
If S = Sum_{x=1}^n then
S p(x) = 128 S 1 + 129/2 S x - 1/2 S x^2
S 1 = n,
S x = n(n+1)/2,
S x^2 = n/6+n^2/2+n^3/3
then
S p(x) = 961n/6+32n^2-n^3/6
.
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- Help: How to calculate quickly this sum 192,255,317....1218,1262?
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- From: Kiuhnm
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- From: gnh888@xxxxxxxxx
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