1000 followers problem - (2) (Easier than the first)
Algebra
Level
4
\[ \begin{eqnarray} S_{n}&=&\displaystyle\sum_{i=1}^{n} a_i \\ S_{n}^{'}&=&\displaystyle \sum_{i=1}^{n} \dfrac{1}{a_i} \\ S(n)&=&\displaystyle\sum_{i=1}^{n} (S_{n}^{'}a_i - 1) \end{eqnarray} \]
I define three kinds of very similar functions as above.
Find the value of \(S(1000)-S_{1000}S_{1000}^{'}\).
Try the first problem here.
Try more of my originals in this set.
by
Nihar Mahajan