In the binomial expansion of [( a - b )^n,,,,n 5,] the sum of 5^th and 6^th terms is zero,…

Question

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

Accepted Answer

According to the question,

t5 + t6 = 0

$$\therefore$$ ${}^n{C_4}.{a^{n - 4}}.{b^4}$ + $$\left( { - {}^n{C_5}.{a^{n - 5}}.{b^5}} \right)$$ = 0

By solving we get,

$${a \over b} = {{n - 4} \over 5}$$

Solutions · 1