Which of the following conditions is sufficient for the uniform convergence of a series of functions $\sum_{n=1}^{\infty} f_n(x)$ on an interval $[a, b]$?
Question 2
Consider the series $\sum_{n=1}^{\infty} a_n$. If the series converges conditionally, which of the following statements must be true?
Question 3
For a series $\sum_{n=1}^{\infty} a_n$, if the Root Test yields $\lim_{n \to \infty} |a_n|^{1/n} = L$, what can be concluded about the convergence of the series if $L = 1$?
Question 4
Which of the following series is an example of a series that converges conditionally?
Question 5
If a series of functions $\sum_{n=1}^{\infty} f_n(x)$ converges uniformly to $S(x)$ on an interval $[a, b]$, and each $f_n(x)$ is continuous on $[a, b]$, what can be concluded about $S(x)$?
