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

If $-\frac{\pi}{2} < \theta < \frac{\pi}{2}$,then $\log \left(\tan \left(\frac{\pi}{4}+\frac{\theta}{2}\right)\right)=$

Let $x \in R$ and $|x| < 1$. Then $\tanh ^{-1} x=$

If $1+\frac{\sqrt{3}-\sqrt{2}}{2 \sqrt{3}}+\frac{5-2 \sqrt{6}}{18}+\frac{9 \sqrt{3}-11 \sqrt{2}}{36 \sqrt{3}}+\frac{49-20 \sqrt{6}}{180}+\ldots$ upto $\infty = 2\left(\sqrt{\frac{b}{a}}+1\right) \log _e\left(\frac{a}{b}\right)$,where $a$ and $b$ are integers with $\operatorname{gcd}(a, b)=1$,then $11 a+18 b$ is equal to ...............

The sum of the series $\log_{4} 2 - \log_{8} 2 + \log_{16} 2 - \dots$ is

$\frac{1}{x + 1} + \frac{1}{2(x + 1)^2} + \frac{1}{3(x + 1)^3} + \dots \infty = $