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| − | Hello, I have a solution to the task 2-34 (TADM2E 2.34) but I have no permissions to created/edit anything.
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| − | Here is the solution:
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| − | This task refers to this song The_Twelve_Days_of_Christmas_(song).
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| − | So we have to calculate the sum like this
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| − | 1 day - 1 gift
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| − | 2 day - 1 gift + 2 gifts
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| − | 3 day - 1 + 2 + 3
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| − | n day - 1 + 2 + 3 + ... + n
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| − | Formula is
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| − | <math>
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| − | \begin{align}
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| − | &\sum_{i=1}^n \sum_{j=1}^n j\
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| − | = \sum_{i=1}^n \frac{n(n+1)}{2} =\\
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| − | &= \frac{1}{2}\sum_{i=1}^n n^2 + \frac{1}{2}\sum_{i=1}^n n=\\
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| − | &= \frac{n(n+1)(2n+1) + 3n(n+1)}{12} = \frac{(n+1)(n^2+2n)}{6}\
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| − | \end{align}
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| − | </math>
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