How to deal with the reciprocal?

Denote \(d_1, d_2, d_3, \ldots , d_n \) as the distinct positive integral divisors of the number \(10500\).

What is the range of the sum: \( \displaystyle S = \sum_{k=1}^{n} \frac 1 {d_k} \)?

Bonus: Find the exact value of \(S\).

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