$\cosh^{-1} 2 = $

The coefficient of $x^n$ in the expansion of $\log_a(1 + x)$ is

Evaluate: $\log_e \sqrt{\frac{1+x}{1-x}}$

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

If $0 < x < 1$ and $y = \frac{1}{2} x^{2} + \frac{2}{3} x^{3} + \frac{3}{4} x^{4} + \dots$,then the value of $e^{1+y}$ at $x = \frac{1}{2}$ is:

If $x, y, z$ are three consecutive positive integers,then $\frac{1}{2}\log_e x + \frac{1}{2}\log_e z + \frac{1}{2xz + 1} + \frac{1}{3}\left( \frac{1}{2xz + 1} \right)^3 + \dots = $