deletions | additions       diff --git a/solving the sum.tex b/solving the sum.tex  index 6e69659..519d837 100644  --- a/solving the sum.tex  +++ b/solving the sum.tex 
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&= a + b(\sqrt{n} - 1) + cn\sum_{p=2}^{\sqrt{n}}\frac{1}{p}+c\sum_{p=2}^{\sqrt{n}}\left[1 - p\right]\\  &= a + b(\sqrt{n} - 1) + cn\left(\sum_{p=1}^{\sqrt{n}}\frac{1}{p} - \sum_{p=1}^{1}\frac{1}{p}\right)+c\left(\sum_{p=2}^{\sqrt{n}}1-\sum_{p=1}^{\sqrt{n}}p + \sum_{p=1}^{1}p\right)\\  &= a + b(\sqrt{n} - 1) + cn(H_{\sqrt{n}} - 1) + c(\sqrt{n} - \frac{\sqrt{n}}{2} - \frac{n}{2})\\  &= a + b(\sqrt{n} - 1) + cn(H_{\sqrt{n}} - 1) + c(\frac{\sqrt{n}}{2} - \frac{n}{2})\\  &= a - b + b\sqrt{n} + cnH_{\sqrt{n}} - cn  \end{split}  \end{equation}