The ratio of the $r^{t h}$ term and the $(r + 1)^{t h}$ term in the expansion of $(1 + x)^{n}$ is

\frac{r}{(n - r + 1) x}

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\frac{1}{(n - r + 1) x}

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\frac{r}{(n - r + 1)}

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\frac{(n - r + 1) x}{r}

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Solution

The correct option is C $\frac{r}{(n - r + 1) x}$
$T_{r}^{t h}$ term $=^{n} C_{r - 1} x^{r - 1}$ ...(i)
And $T_{r + 1}$ th term $=^{n} C_{r} x^{r}$ ...(ii)
Therefore, $\frac{T_{r}}{T_{r + 1}}$
$= \frac{^{n} C_{r - 1} x^{r - 1}}{^{n} C_{r} x^{r}}$
$= \frac{^{n} C_{r - 1}}{^{n} C_{r} x}$
$= \frac{r}{(n - (r - 1)) x}$
$= \frac{r}{(n - r + 1) x}$

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