Convergence to zero of a specific infinite product

Question

Maybe less ambitious but I would be happy to prove the following. I have tried but without success.

Thanks for any help

Answer 1

Hint: $$ \lim_{n \to \infty} (1-1/n)^n = 1/e$$ What does this tell you about the limit of $(1-1/n)^{8n+4}$?