## Calculus: Early Transcendentals (2nd Edition)

$\{0.2^n\}$ converges to $0$. The sequence is monotonic.
The general form of a geometric sequence is $a^r$. Since $a < 1$: $$\lim\limits_{n \to \infty} 0.2^n = 0$$ In addition, because $a<1$, the sequence is non increasing and thus is monotonic.