Proving Cauchy sequences

\(\left\{\dfrac{1}{n}\right\}\) is a Cauchy sequence.
\(\left\{\dfrac{n^2}{n^2 + 1}\right\}\) is a Cauchy sequence.
\(\left\{\sin\left(\dfrac{1}{n}\right)\right\}\) is a Cauchy sequence.
\(\left\{\cos\left(\dfrac{1}{n}\right)\right\}\) is a Cauchy sequence.

YouTube videos