# Math Help - analysis

1. ## analysis

$\mbox {Let x_n be an unbounded sequence .prove that there is a subsequence x_{n_k }$
$\mbox {of x_n
such that \frac {1}{x_{n_k}} \to ^k 0$

2. Originally Posted by flower3
$\mbox {Let x_n be an unbounded sequence .prove that there is a subsequence x_{n_k }$
$\mbox {of x_n
such that \frac {1}{x_{n_k}} \to ^k 0$
We may as well assume the sequence is not bounded above.
$\left( {\exists x_{n_1 } } \right)\left[ {x_{n_1 } > \max \left\{ {1,x_1 } \right\}} \right]$.
$\left( {\forall j > 1} \right)\left( {\exists x_{n_j } } \right)\left[ {x_{n_j } > \max \left\{ {j,x_{n_{j - 1} } } \right\}} \right]$.