Question

用比值审敛法求下列级数的收敛性

Answer 1

[(n+1)!/(n+1)^(n+1)]/[n!/n^n]

=(n+1)n^n/(n+1)^(n+1)

=n^n/(n+1)^n

=1/(1+1/n)^n

当n趋向于无穷大时,该值趋向于1/e