Limits, Cauchy seq's: sqrt[3](n+4/(8n+1)), sum (sin(k)/(k^3)

[waciz]

I really need help finding and proving these limits

1) \lim_{n \rightarrow \infty}\sqrt[3]{\frac{n+\frac1{4}}{{8n+1}}

2) \lim_{n \rightarrow \infty}\sqrt{{n^2}-1}-n-1

3) \lim_{n \rightarrow \infty}\frac{n^2+1}{2n+1}-\frac{3n^2+1}{6n+1}

And prooving that this is a Cauchy sequence
1) \sum_{k=1}^n k = \frac{sink}{k^3}

1)

2)

3)

And prooving that this is a Cauchy sequence

1)

 

[stapel]

What are your thoughts? What have you tried? How far did you get? Where are you stuck?

Please be complete. Thank you!

Eliz.