Find the coefficient of $x^{r}$ in the expansion of $(1 - x)^{- n}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B

$T_{r + 1}$ = $\frac{(- n) (- n - 1) (- n - 2) . . . . . (- n - r + 1)}{r!} \times (- x)^{r}$

Coefficient of $x r$

= $(- 1)^{r} \frac{(n) (n + 1) (n + 2) . . . .}{r!} (n + r - 1) \times (- 1)^{r}$

= $(- 1)^{2 r} \times \frac{(n - 1)! \times (n) (n + 1) . . . . . . . (n + r - 1)}{(n - 1)! \times r!}$

= $\frac{(n + r - 1)!}{((n + r - 1) - r! \times r)}$

= $n + r -^{1} C_{r}$

Suggest Corrections

Similar questions

x^{r}

\frac{(1 - x)^{2}}{(1 + x)^{3}}

x^{r}

{(x^{2} + \frac{1}{x^{2}})}^{n}

x^{r}

\frac{1 - a x - x^{2}}{e^{x}}

x^{r}

{(x + \frac{1}{x})}^{n}

x^{r}

1 + (1 + x) + (1 + x)^{2} + . . . . . + (1 + x)^{n}

^{n + 1} C_{r + 1}

Join BYJU'S Learning Program