I have to find the radius of convergence of some power series but I find myself in trouble for three of them : the series are
For the first one I have tried the Ratio Test for series first but I don't kow how to deal with the factorials as exponents... For the second one, I'm tempted to say it never converges but I cannot prove it. And for the last one, I'd say it converges for $|x|< 1$ since $-1<\sin(h)<1$ anyway, but I'm not quite sure...
Some hints would help a lot! Thank you.