$1 + \frac{a - bx}{1!} + \frac{(a - bx)^2}{2!} + \frac{(a - bx)^3}{3!} + \dots \infty = $

The coefficient of $x^n$ in $\frac{1-2x}{e^x}$ is:

The money invested in a company is compounded continuously. ₹ $400$ invested today becomes ₹ $800$ in $6$ years. What will it become at the end of $33$ years? (Given $\sqrt{2} \approx 1.4142$)

The sum of the series $C = 1 + \frac{\cos x}{1!} + \frac{\cos 2x}{2!} + \frac{\cos 3x}{3!} + \dots$ and $S = \frac{\sin x}{1!} + \frac{\sin 2x}{2!} + \frac{\sin 3x}{3!} + \dots$ is equal to

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

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