Let $k$ be a field and $x$ is transcendental over $k$. Can we construct a pseudo-cauchy sequence $(a_{i})$ convergent to $x$ with each $a_{i}$ is algebraic over $k$ and $k(a_{i})\subseteq k(a_{i + 1})$. Thanks

Is your question whether such a $k$ and $x$ exist, or whether a sequence can be found for any given $k$ and $x$ of the form you describe?
– Yemon ChoiJan 11 '13 at 1:19

@ Yemon, thanks. I am looking whether a sequence exist or not for any given $k$ and $x$.
– RajnishJan 11 '13 at 2:49