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sumfor(n, 2, 100, (log(n) / log(100!)) = 157.97 / 157.97 = 1

$\sum \limits_{k=2}^{100}\dfrac{1}{\log_k(100!)} = \\ \sum \limits_{k=2}^{100}\dfrac{\log(k)}{\log(100!)} = \\ \sum \limits_{k=2}^{100}\dfrac{\log(k)}{\sum \limits_{j=2}^{100}\log(j)} =\\ \dfrac{\sum \limits_{k=2}^{100} \log(k)}{\sum \limits_{j=2}^{100} \log(j)} = \\ 1$