radius of convergence

hey there, im trying to find the radius of convergence for the series 1+px+p(p-1)x^2/2!+p(p-1)(p-2)x^3/3!+... but i have no idea even where to begin. thanks for the help

Just use the ratio test.

thats what ive been trying to do, i just dont know what formula would make up the series to use the test. since p is a constant, would it be sum: p!*x^n/n! ? but that doesnt seem right to me, i dont think it should be p!

1+px+p(p-1)x^2/2!+p(p-1)(p-2)x^3/3!+...
= U0 + U1 + U2 + U3...

|Un+1/Un| = |(P-N+1)x/N|  which tends to |x| as N tends to infinity. ie. converges if |x| < 1, diverges if |x| > 1.

So your radius of convergence is 1.