I was trying to make some undergraduate level analysis problem. The point was interval of convergence of power series. It seems that the students are bored with usual coefficients. So I considered the following 'relatively' new kind of power series. $$ f(x) = \sum_{n=1}^\infty \left( 1-\frac{1}{n}\right)^{n^2} x^n $$ The question I proposed is to find the interval of convergence of $f(x)$. Soon after, I realized using this series I can make rather interesting questions.
Prove that $\lim_{x \rightarrow e^-} f(x) = \infty$ and find the limit $\lim_{x \rightarrow -e^+} f(x)$.
I think this maybe an interesting question for undergraduate students. However I have failed to make a reasonable solution. Please help me to improve this questions.