Tcaner: /* Proposed solution (with steps) */

2018-12-12T07:34:45Z

‎Proposed solution (with steps)

Mardurhack: Created page with " == 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 distan..."

2014-12-13T00:45:08Z

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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== 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 distance in the progression is 1 and the coefficient is also 1.

<math>\sum\limits_{i=1}^{n/2} \sum\limits_{j=i}^{n-i} j</math>

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>

We can rule out the constants.

<math>n*\frac{1}{2}*\sum\limits_{i=1}^{n/2} (n - i)</math>

We can now use the linearity of summations to get simpler ones.

<math>n*\frac{1}{2}*[\sum\limits_{i=1}^{n/2} n - \sum\limits_{i=1}^{n/2} i]</math>

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 <math>\frac{n}{2}</math>.

The rest is just numerical calculations. The problem is that I cannot get to the answer on the main page: <math>\frac{n^3}{8}</math>. Could somebody help me catch the error? Thank you in advance.

--[[User:Mardurhack|Mardurhack]] ([[User talk:Mardurhack|talk]]) 19:45, 12 December 2014 (EST)

@@ Line 10: / Line 10: @@
 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.

Talk:TADM2E 2.36 - Revision history

Tcaner: /* Proposed solution (with steps) */

Mardurhack: Created page with " == 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 distan..."

Mardurhack: Created page with " == 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 distan..."