Question

The coefficient of $x^{n}$ in the expansion of $\log_{a}(1 + x)$ is.

• A. $\frac{( - 1)^{n - 1}}{n}$
• B. $\frac{( - 1)^{n - 1}}{n}\log_{a}e$
• C. $\frac{( - 1)^{n - 1}}{n}\log_{e}a$
• D. $\frac{( - 1)^{n}}{n}\log_{a}e$

Answer 1

Answer: (B)

$\frac{( - 1)^{n - 1}}{n}\log_{a}e$

Answer 2

We have $\frac{1^{r}}{1!} + \frac{2^{r}}{2!} + \frac{3^{r}}{3!} + .....$

$1 + \frac{1}{1!} + \frac{1}{2!} + .... + \frac{1}{r!}$

Therefore coefficient of $\frac{1}{r!}\left\lbrack \frac{1^{r}}{1!} + \frac{2^{r}}{2!} + \frac{3^{r}}{3!} + .... \right\rbrack$in $\frac{e^{r}}{r!}$ is$T_{n} = \frac{3^{n}}{2(n!)} - \frac{1}{2(n!)},$.