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General Term of Binomial Expansion

Find the r+1t...

Question

Find the $(r + 1)^{t h}$ term in the expansion of $(x + y)^{n}$

A

$^{n} C_{r + 1} x^{n - r - 1} y^{r + 1}$

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B

$^{n} C_{r} x^{n - r} y^{r}$

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C

$^{n} C_{r - 1} x^{n - r + 1} y^{r - 1}$

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D

$^{n} C_{r} x^{n - r} y^{r - 1}$

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Solution

The correct option is B
$^{n} C_{r} x^{n - r} y^{r}$

There will be (n+1) terms in the expansion of $(x + y)^{n}$
The first term will be $^{n} C_{0} x^{n} y^{0}$ and the last term or $(n + 1)^{t h}$ term will be $^{n} C_{n} x^{0} y^{n}$ . If you observe more terms, you will find out that
$T_{r + 1} =^{n} C_{r} x^{n - r} y^{r}$

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