deletions | additions       diff --git a/d) Quicksort average complexity.tex b/d) Quicksort average complexity.tex  index 4abe48f..20d3a39 100644  --- a/d) Quicksort average complexity.tex  +++ b/d) Quicksort average complexity.tex 
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\Updownarrow\\  \frac{C(n)}{\prod_{k=0}^{n-1}\left[1+\frac{1}{k+1}\right]} - \frac{C(0)}{\prod_{k=0}^{-1}\left[1+\frac{1}{k+1}\right]} = \sum_{m=0}^{n-1}\left[\frac{2 - \frac{1}{m+1}}{\prod_{k=0}^{m}\left[1+\frac{1}{k+1}\right]}\right]\\  \Updownarrow\\  C(n) = \left(\prod_{k=0}^{n-1}\left[1+\frac{1}{k+1}\right]\right)\left(C(0) \left(\prod_{k=0}^{n-1}\left[1+\frac{1}{k+1}\right]\right)\left(\frac{C(0)}{\prod_{k=0}^{-1}\left[1+\frac{1}{k+1}\right]}  + \sum_{m=0}^{n-1}\left[\frac{2 - \frac{1}{m+1}}{\prod_{k=0}^{m}\left[1+\frac{1}{k+1}\right]}\right]\right)\\ \Updownarrow\\  C(n) = \left(n+1\right)\left(C(0) + \sum_{m=0}^{n-1}\left[\frac{2 - \frac{1}{m+1}}{n+2}\right]\right)  \]