Answer
(a) A sequence is an ordered list of numbers which stem from some sequence term $a_{n}$
For example: $\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},...$
With a series, we actually take this list of terms and add them.
This is the purpose for the capital Greek letter sigma $\Sigma$
For example: $\Sigma a_{n}=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5},...$
(b) A convergent series is a series where the sum of all of its terms is finite. A divergent series is a series where the sum of all of its terms is infinite or its n-th partial sum does not approach a finite number as $n \to \infty $.
Work Step by Step
(a) A sequence is an ordered list of numbers which stem from some sequence term $a_{n}$
For example: $\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},...$
With a series, we actually take this list of terms and add them.
This is the purpose for the capital Greek letter sigma $\Sigma$
For example: $\Sigma a_{n}=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5},...$
(b) A convergent series is a series where the sum of all of its terms is finite. A divergent series is a series where the sum of all of its terms is infinite or its n-th partial sum does not approach a finite number as $n \to \infty $.
