In the binomial expansion of a-bn- n - 5- sum of 5th and 6th terms is zero- then a-b equals5-n-4B- n-46-n-5-n-5 C- n-5-6D- n-4-5

The correct option is D Given T_5+T_6=0 ⇒ ^nC_4 a^n 4 b^4 ^nC_5 a^n 5b^5=0 ⇒ ^nC_4 a^n 4b^4= ^nC_5 a^n 5 b^5 ⇒a^n 4b^4/a^n 5b^5=^nC_5/^nC_4⇒a/b=n 5+1/5⇒a/b ...

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Byju's Answer

Standard XII

Mathematics

Greatest Binomial Coefficients

In the binomi...

Question

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

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Solution

The correct option is D

$G i v e n T_{5} + T_{6} = 0 \Rightarrow^{n} C_{4} a^{n - 4} b^{4} -^{n} C_{5} a^{n - 5} b^{5} = 0 \Rightarrow^{n} C_{4} a^{n - 4} b^{4} =^{n} C_{5} a^{n - 5} b^{5}$

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

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In the binomial expansion of (a–b)n,n≥5, sum of 5th and 6th terms is zero, then ab equals

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