Tomorrow I have an exam on mathematical analysis and I solving exams task from earlier years, and here is:
Find limit of: $\lim_{n \to \infty} \frac{(4n^3 + 1)(4n - 2)!n\sin{\frac{2}{n}}}{(4n + 1)!+3} $
I checked in Wolfram Alpha and Maxima that it is $\frac{1}{8}$ but how to get this? I have tried almost everything I remember but still cannot find solution.
Firstly, sorry for the title, but I have no idea how to describe this shorter.