## Calculus 8th Edition

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.