# Convergence of Subsequences

• Apr 11th 2012, 12:34 PM
renolovexoxo
Convergence of Subsequences
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.
• Apr 14th 2012, 05:36 PM
Sudharaka
Re: Convergence of Subsequences
Hi renolovexoxo,

The easiest way to construct such a sequence is to define all the even terms as one and odd terms as zero (or vice versa).

$x_n=\begin{cases}1&\mbox{ if }n=2k\mbox{ where }k\in\mathbb{Z}^{+}\\0&\mbox{ if }n=2k+1\mbox{ where }k\in\mathbb{Z}^{+}\cup\{0\}\end{cases}$