Difference between revisions of "Talk:TADM2E 2.36"
Mardurhack (talk | contribs) (Created page with " == Proposed solution (with steps) == <math>\sum\limits_{i=1}^{n/2} \sum\limits_{j=i}^{n-i} \sum\limits_{k=1}^{j} 1</math> The innermost summation is just j since the distan...") |
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For the middle summation we can use Gauss' rule. | For the middle summation we can use Gauss' rule. | ||
| − | <math>\sum\limits_{i=1}^{n/2} \frac{1}{2} * (n - i) * (n - i + i) = \sum\limits_{i=1}^{n/2} \frac{1}{2} * (n - i) * (n)</math> | + | <math>\sum\limits_{i=1}^{n/2} \frac{1}{2} * (n - i) * (n - i + i) = \sum\limits_{i=1}^{n/2} \frac{1}{2} * (n - i) * (n)</math> // This line must be way off |
We can rule out the constants. | We can rule out the constants. | ||
Latest revision as of 07:34, 12 December 2018
Proposed solution (with steps)
$ \sum\limits_{i=1}^{n/2} \sum\limits_{j=i}^{n-i} \sum\limits_{k=1}^{j} 1 $
The innermost summation is just j since the distance in the progression is 1 and the coefficient is also 1.
$ \sum\limits_{i=1}^{n/2} \sum\limits_{j=i}^{n-i} j $
For the middle summation we can use Gauss' rule.
$ \sum\limits_{i=1}^{n/2} \frac{1}{2} * (n - i) * (n - i + i) = \sum\limits_{i=1}^{n/2} \frac{1}{2} * (n - i) * (n) $ // This line must be way off
We can rule out the constants.
$ n*\frac{1}{2}*\sum\limits_{i=1}^{n/2} (n - i) $
We can now use the linearity of summations to get simpler ones.
$ n*\frac{1}{2}*[\sum\limits_{i=1}^{n/2} n - \sum\limits_{i=1}^{n/2} i] $
In the first summation n is just a constant so we can bring it outside and the for the second summation we use, once again, Gauss' rule. The first summation turns into $ \frac{n}{2} $.
The rest is just numerical calculations. The problem is that I cannot get to the answer on the main page: $ \frac{n^3}{8} $. Could somebody help me catch the error? Thank you in advance.
--Mardurhack (talk) 19:45, 12 December 2014 (EST)
