Does the sequence $c_n=\frac{4n^2+1}{n^2+9}$ converge?

Evaluate the limit of the sequence $c_n={\tan }^{-1}\left(\frac{12n}{12n+6}\right)$ as $n\to \infty$.

Determine the limit as $n\to \infty$ of the sequence $d_n=\frac{\sqrt{16n^4-8n}}{20n^2+4}$, or state if it diverges.

A scientist injects $150\text{ mg}$ of a substance into a test subject. Each hour, $8\%$ of the substance is removed from the body. Let $s_n$ be the amount of substance remaining after $n$ hours, where $s_0=150$ $\text{mg}$. What is the explicit formula for the sequence $s_n$?

Let $\left\{a_n\right\}=\{3,\frac{3}{2},\frac{3}{3},\frac{3}{4},\dots \}$ and $\left\{b_n\right\}=\{3,0,\frac{3}{2},0,\frac{3}{3},0,\frac{3}{4},0,\dots \}$. Are the limits $\underset{n\to \infty }{\lim }{a}_n$ and $\underset{n\to \infty }{\lim }{b}_n$ equal?