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Binomial Theorem

If T 2 / T...

Question

If $\frac{T_{2}}{T_{3}}$ in the expansion of $(a + b)^{n}$ and $\frac{T_{3}}{T_{4}}$ in the expansion of $(a + b)^{n + 3}$ are equal, then n is equal to-

3

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4

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5

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6

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Solution

The correct option is D $5$
$T_{2} =^{n} C_{1} a^{n - 1} b^{1}$ $T_{3} =^{n + 3} C_{2} a^{n + 1} b^{2}$
$T_{3} =^{n} C_{2} a^{n - 2} b^{2}$ $T_{4} =^{n + 3} C_{3} a^{n} b^{3}$
$\frac{T_{2}}{T_{3}} = \frac{2}{(n - 1)} \frac{a}{b}$ $\frac{T_{3}}{T_{4}} = \frac{3}{(n + 1)} \frac{a}{b}$
$2 / (n - 1) = 3 / (n + 1)$
$\Rightarrow n = 5$ .

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