1000 followers problem - (2) (Easier than the first)

Algebra Level 4

$\begin{aligned} S_{n}&=&\displaystyle\sum_{i=1}^{n} a_i \\ S_{n}^{'}&=&\displaystyle \sum_{i=1}^{n} \dfrac{1}{a_i} \\ S(n)&=&\displaystyle\sum_{i=1}^{n} (S_{n}^{'}a_i - 1) \end{aligned}$

I define three kinds of very similar functions as above.

Find the value of $S(1000)-S_{1000}S_{1000}^{'}$ .

1000 followers problem - (2) (Easier than the first)

Try the first problem here.

Try more of my originals in this set.