Convergence of Subsequences

[renolovexoxo]

Construct a sequence xn (from one to infinity) such that it contains one subsequence that converges to 1 and another subsequence which converges to 0.

 

[pka]

Construct a sequence xn (from one to infinity) such that it contains one subsequence that converges to 1 and another subsequence which converges to 0.

\(\displaystyle {x_n} = \left\{ {\begin{array}{rl} {\frac{1}{n},}&{\text{n even}} \\
{1 - \frac{1}{n},}&{\text{n odd}}
\end{array}} \right.\)