**a.**\(\displaystyle l=\lim_{N\rightarrow \infty } \underbrace{sinsin...sin}_{N}N\).

**b.**\(\displaystyle l=\lim_{n\rightarrow \infty } n!^{-2n}\prod_{i=1}^{n}i^i \).

**c.**\(\displaystyle l=\lim_{n\rightarrow \infty } \frac{\sum_{i=1}^{n^2 }i^{-1}}{\ln(n)}\).