let be an unbounded sequence . prove that there is a subsequence of such that
Follow Math Help Forum on Facebook and Google+
If epsilon > 0 then 1/x_n - 0 < epsilon => x_n > 1/epsilon. If you choose a strictly increasing subsequence of {x_n} (which is possible since it is unbounded), then all but a finite number of x_n > 1/epsilon, so 1/x_n converges to 0.
Originally Posted by flower3 let be an unbounded sequence . prove that there is a subsequence of such that Suppose that is not bounded above. Then . Let then . Now you can see how to construct the required subsequence.
View Tag Cloud