# My favourite summation

Calculus Level 4

$\large \sum_{x\in S}\frac{1}{x-1}=\frac{1}{3}+\frac{1}{7}+\frac{1}{8}+\frac{1}{15}+\frac{1}{24}+\ldots$

Find the value of the above summation when it's summed over all elements in set $$S$$.

Set $$S$$ consists of all perfect powers excluding 1 and excluding duplicates.

$S=\{4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100,...\}$

• A perfect power is a number of the form $$m^n$$ where $$m$$ and $$n$$ are natural numbers and $$n\neq 1$$.

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