If a sequence is both bounded and monotonic, then the sequence converges.

1. Find the limit as n approaches infinity. 2. If the limit exists and is finite, it converges. 3. If the limit does not exist or is infinite, it diverges.

1. Calculate $a_1, a_2, a_3$. 2. $s_1 = a_1$. 3. $s_2 = a_1 + a_2$. 4. $s_3 = a_1 + a_2 + a_3$.

$${a_n}^\infty_1$$

$$s_n = \sum_{i=1}^{n} a_i$$

$$s_\infty = \lim\limits_{n \to \infty} \sum_{i=1}^{n} a_i$$