Answer
(a) A convergent {$a_n$} is convergent if $\lim\limits_{n \to \infty}a_n$ exists. That is, the terms of the sequence approach to a unique number.
(b) A series $\Sigma{a_n}$ is convergent if $\lim\limits_{n \to \infty}s_n$ exists, where $s_n=\Sigma_{i=1}^na_i$ .
(c) It means the sequence converges to $3$ . That is, either the terms of the sequence approach $3$ or, they are exactly $3$ . For example: {$1,2,3,3,3,3,3,3....$}
(d) It means the series converges to $3$ . That is, the sum of all the terms converges to $3$ or is exactly $3$.
Work Step by Step
(a) A convergent {$a_n$} is convergent if $\lim\limits_{n \to \infty}a_n$ exists. That is, the terms of the sequence approach to a unique number.
(b) A series $\Sigma{a_n}$ is convergent if $\lim\limits_{n \to \infty}s_n$ exists, where $s_n=\Sigma_{i=1}^na_i$ .
(c) It means the sequence converges to $3$ . That is, either the terms of the sequence approach $3$ or, they are exactly $3$ . For example: {$1,2,3,3,3,3,3,3....$}
(d) It means the series converges to $3$ . That is, the sum of all the terms converges to $3$ or is exactly $3$.
