1. The problem statement, all variables and given/known data Show that an increasing sequence is convergent if it has a convergent subsequence. 3. The attempt at a solution Suppose xjn is a subsequence of xn and xjn→x. Therefore [itex]\exists[/itex]N such that jn>N implies |xjn-x|<[itex]\epsilon[/itex] It follows that n>jn>N implies |xn-x|<[itex]\epsilon[/itex] Therefore xn→x The solution that I've been given is much more complicated I'm just wondering whether my simpler solution is also correct.