Answer
(a)
The $n$ th partial sum $S_{n}$ of a sequence $a_{1}, a_{2}, a_{3}, \ldots$ is
obtained by adding the first $n$ terms of the sequence
$$S_{1}=a_{1}, S_{2}=a_{1}+a_{2}, \ldots,$$
and in general
$$S_{n}=a_{1}+a_{2}+\cdots+a_{n}$$
---
(b)
$\text{ the first three partial sums of the sequence given by }$$ \rightarrow \ [\ a_{n}=1 / n \ ].$
$$S_{1}=1,$$
$$ S_{2}=\frac{3}{2},$$
$$ S_{3}=\frac{11}{6}$$
Work Step by Step
(a)
The $n$ th partial sum $S_{n}$ of a sequence $a_{1}, a_{2}, a_{3}, \ldots$ is
obtained by adding the first $n$ terms of the sequence
$$S_{1}=a_{1}, S_{2}=a_{1}+a_{2}, \ldots,$$
and in general
$$S_{n}=a_{1}+a_{2}+\cdots+a_{n}$$
---
(b)
$\text{ the first three partial sums of the sequence given by }$$ \rightarrow \ [\ a_{n}=1 / n \ ].$
$$S_{1}=\frac{1}{1}=1,$$
$$ S_{2}=\frac{1}{1}+\frac{1}{2}=\frac{3}{2},$$
$$ S_{3}=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}=\frac{11}{6}$$
