a_1 =−(1/(30)) a_2 =−(1/(12)) a_3 =−(1/6) a_4 =−(7/(24)) a_5 =−(7/(15)) a_6 =−(7/(10)) a_7 =−1 find a


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Question Number 95048 by Tony Lin last updated on 22/May/20

$a_{1} = - \frac{1}{30}$ $a_{2} = - \frac{1}{12}$ $a_{3} = - \frac{1}{6}$ $a_{4} = - \frac{7}{24}$ $a_{5} = - \frac{7}{15}$ $a_{6} = - \frac{7}{10}$ $a_{7} = - 1$ $f i n d a_{k}$
Commented by Tony Lin last updated on 22/May/20

$a_{1} = \frac{1}{5} C_{4}^{5} (- \frac{1}{30})$ $a_{2} = \frac{1}{6} C_{4}^{6} (- \frac{1}{30})$ $a_{3} = \frac{1}{7} C_{4}^{7} (- \frac{1}{30})$ $a_{k} = \frac{1}{k + 4} C_{4}^{k + 4} (- \frac{1}{30})$ $= \frac{(k + 4)!}{(k + 4) 4! k!} (- \frac{1}{30})$ $= - \frac{(k + 1) (k + 2) (k + 3)}{720}$
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