Find the Maclaurin series for f(x)=sinh(x)=ex−e−x2f(x) = \sinh(x) = \frac{e^x - e^{-x}}{2}f(x)=sinh(x)=2ex−e−x. Which statement(s) is/are correct?
The series contains only odd powers: sinh(x)=x+x33!+x55!+⋯\sinh(x) = x + \frac{x^3}{3!} + \frac{x^5}{5!} + \cdotssinh(x)=x+3!x3+5!x5+⋯
The series is ∑n=0∞x2n+1(2n+1)!\sum_{n=0}^{\infty} \frac{x^{2n+1}}{(2n+1)!}∑n=0∞(2n+1)!x2n+1
The radius of convergence is R=∞R = \inftyR=∞ (converges everywhere)
The coefficient of x4x^4x4 is 14!\frac{1}{4!}4!1