Answer
a)
A sequence {$a_{n}$} is convergent if $\lim\limits_{n \to \infty}a_{n}$ exists. That is, if 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 $s_{n} = \Sigma^{n}_{i=1}a_{i}$. (Note: $s_{n}$ is called the $n$th partial sum, i.e., the sum of the first $n$ terms.)
c)
It means the sequence converges to 3. That is, either the terms of the sequence approach 3 or they are exactly 3 (starting at some point). For example, {$2,2.9,2.99,2.999,2.9999,...$} and {$1,2,3,3,3,3,...$}.
d)
It means that the series converges to 3. The sum of all the terms converge to 3 or is exactly 3.
Work Step by Step
a) definition of a convergent sequence
b) definition of a convergent series
c) explanation above
d) explanation above
