Answer
Diverges
Work Step by Step
Given: ${0,1,0,0,1,0,0,0,1,....}$
A sequence converges if and only if $\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty}a_{n+1}$
Since,
$\lim\limits_{n \to \infty}a_n\ne\lim\limits_{n \to \infty}a_{n+1}$
Therefore, the given sequence does not converge.
Hence, it has no limit, so diverges.
