If in expansion of ${(1 + x)}^{21}$, the coefficient of $x^{r}$ and $x^{r + 1}$ be equal, then $r$is equal to

Question

Dr. Abubacker · Accepted Answer

(b)
According to question, coefficient of $x^{r} =$coefficient of $x^{r + 1}$
$\Longrightarrow \ ^{21}C_{r} = \ ^{21}C_{r + 1}$ …(i)
But $\ ^{21}C_{r} = \ ^{21}C_{21 - r}\ \ \ \ \ \ \ \ \ \ \ \$…(ii)
On comparing Eqs. (i) and (ii), we get
$r + 1 = 21 - r \Longrightarrow r = \frac{21 - 1}{2} = 10$

Q. If in expansion of ${(1 + x)}^{21}$, the coefficient of $x^{r}$ and $x^{r + 1}$ be equal, then $r$is equal to

Explanation

Reviewed by Dr. Abubacker

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