If $|x| < 1$,then the coefficient of $x^5$ in the expansion of $(1 - x) \ln(1 - x)$ is

If $P = 1 + \frac{1}{2 \times 2} + \frac{1}{3 \times 2^{2}} + \dots$ and $Q = \frac{1}{1 \times 2} + \frac{1}{3 \times 4} + \frac{1}{5 \times 6} + \dots$, then

The value of $\log_e \left( 1 + ax^2 + a^2 + \frac{a}{x^2} \right)$ is

For $|x| < 1$,the coefficient of $x^3$ in the expansion of $\log(1+x+x^2)$ in ascending powers of $x$ is (in $/3$)

Evaluate the sum of the series: $\log_e \frac{4}{5} + \frac{1}{4} - \frac{1}{2} \left( \frac{1}{4} \right)^2 + \frac{1}{3} \left( \frac{1}{4} \right)^3 - \dots$

$\frac{m - n}{m + n} + \frac{1}{3}\left( \frac{m - n}{m + n} \right)^3 + \frac{1}{5}\left( \frac{m - n}{m + n} \right)^5 + \dots \infty = $