In the binomial expansion of ((a - b)^n, n \>= 5,) a the sum... | Mathematics | SolveeIt

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

$\frac{5}{n-4}$

$\frac{6}{n-5}$

$\frac{n-5}{6}$

$\frac{n-4}{5}$

Answer

$\frac{n-4}{5}$

Explanation

$^{n}C_{4}\,a^{n-4}\left(-b\right)^{4}+^{n}C_{5}\,a^{n-5}\left(-b\right)^{5}=0$ $\Rightarrow \left(\frac{a}{b}\right)=\frac{n-5+1}{5}.$

Mathematics Question on Binomial theorem