Problem 1128 (difficulty: 3/10)

For which values of \(\displaystyle x\) do the following sequences converge? On which intervals do they converge uniformly?

\(\displaystyle \root{n}\of{|x|} \qquad \frac{x^n}{n!} \qquad x^n-x^{n+1} \qquad \left(1+\frac{x}n\right)^n \)

Give me another random problem!