# Difference between revisions of "TADM2E 2.34"

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(Created page with "This task refers to this song The_Twelve_Days_of_Christmas_(song) So we have to calculate the sum like this 1 day - 1 gift 2 day - 1 gift + 2 gifts 3 day - 1 + 2 + 3 n day -...") |
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This task refers to this song The_Twelve_Days_of_Christmas_(song) | 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 | So we have to calculate the sum like this | ||

1 day - 1 gift | 1 day - 1 gift | ||

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2 day - 1 gift + 2 gifts | 2 day - 1 gift + 2 gifts | ||

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3 day - 1 + 2 + 3 | 3 day - 1 + 2 + 3 | ||

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n day - 1 + 2 + 3 + ... + n | n day - 1 + 2 + 3 + ... + n | ||

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Formula is | Formula is |

## Latest revision as of 07:08, 27 May 2020

This task refers to this song The_Twelve_Days_of_Christmas_(song)

So we have to calculate the sum like this

1 day - 1 gift

2 day - 1 gift + 2 gifts

3 day - 1 + 2 + 3

n day - 1 + 2 + 3 + ... + n

Formula is

$ \begin{align} &\sum_{i=1}^n \sum_{j=1}^n j\ = \sum_{i=1}^n \frac{n(n+1)}{2} =\\ &= \frac{1}{2}\sum_{i=1}^n n^2 + \frac{1}{2}\sum_{i=1}^n n=\\ &= \frac{n(n+1)(2n+1) + 3n(n+1)}{12} = \frac{(n+1)(n^2+2n)}{6}\ \end{align} $