In the binomial expansion of ( a - b ) n , n 5 , the sum of the 5th and 6th terms is zero. Then a b equals [2001]

Question

In the binomial expansion of ${(a - b)}^{n}, n \geq 5,$ the sum of the 5th and 6th terms is zero. Then $\frac{a}{b}$ equals [2001]

Smart Achievers · Accepted Answer

(2)

$In binomial expansion {(a - b)}^{n}, n \geq 5;$

$T_{5} + T_{6} = 0$

$\Rightarrow {}^{n}C_{4} a^{n - 4} b^{4} - {}^{n}C_{5} a^{n - 5} b^{5} = 0$

$\Rightarrow \frac{{}^{n}C_{4}}{{}^{n}C_{5}} \cdot \frac{a}{b} = 1$

$\Rightarrow \frac{5}{n - 4} \cdot \frac{a}{b} = 1$

$\Rightarrow \frac{a}{b} = \frac{n - 4}{5}$

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