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, 08:05, 20 May 2015
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| </math> | | </math> |
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− | Because <math>a_k</math> may be 0, we will see cases of <math>\binom{k-1}{-1}</math> when <math>a_k=0</math>. This is alright because of the definition of <math>\binom{n}{r}</math>. | + | Because <math>a_k</math> may be 0, we will see cases of <math>\binom{k-1}{-1}</math> when <math>a_k=0</math>. This is alright because of the definition of <math>\binom{n}{r}</math> which defines this case as 0. |
| But to make it more sensible, we can define the function equivalently as: | | But to make it more sensible, we can define the function equivalently as: |
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| \end{align} | | \end{align} |
| </math> | | </math> |
| + | |
| + | So when <math>a_k=0</math>, the binomial coefficient reads as <math>\binom{k-1}{k}</math> which is equals to since there are 0 ways to choose k items from k-1 items. |
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| = Simple cases = | | = Simple cases = |