In binomial expansion of {left( {a - b} right)^n},n ge 5, sum of 5^{th} and 6^{th} terms is zero , t

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7.Binomial Theorem

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In the binomial expansion of ${\left( {a - b} \right)^n},n \ge 5,\;$ the sum of $5^{th}$ and $6^{th}$ terms is zero , then $a/b$ equals.

A

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

B

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

C

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

D

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

(AIEEE-2007) (IIT-2001)

Solution

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

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

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

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

Standard 11

Mathematics

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