Question

The coefficient of $x^{r}$ in the expansion of

$1 + \frac{a + bx}{1!} + \frac{(a + bx)^{2}}{2!} + ..... + \frac{(a + bx)^{n}}{n!} + .....$ is.

• A. $\frac{(a + b)^{r}}{r!}$
• B. $\frac{b^{r}}{r!}$
• C. $\frac{e^{a}b^{r}}{r!}$
• D. $e^{a + b^{r}}$

Answer 1

Answer: (C)

$\frac{e^{a}b^{r}}{r!}$

Answer 2

$\frac{e^{x} + 1}{x + 1}$

The coefficient of$\frac{e^{x} + 1}{x - 1}$.