If $2 \sinh x = \cosh x$,then $x =$

For every real number $x$, let $f(x) = \frac{x}{1!} + \frac{3}{2!} x^2 + \frac{7}{3!} x^3 + \frac{15}{4!} x^4 + \dots$. Then the equation $f(x) = 0$ has

In the expansion of $\frac{a + bx}{e^x}$,the coefficient of $x^r$ is

$\frac{\frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!} + \dots \infty}{1 + \frac{1}{3!} + \frac{1}{5!} + \frac{1}{7!} + \dots \infty} = $

The sum of the series $\frac{4}{1!} + \frac{11}{2!} + \frac{22}{3!} + \frac{37}{4!} + \frac{56}{5!} + \dots$ is

$\frac{2}{2!} + \frac{2+4}{3!} + \frac{2+4+6}{4!} + \dots$ is equal to