deletions | additions       diff --git a/solving the sum.tex b/solving the sum.tex  index 7f618bb..3c106d2 100644  --- a/solving the sum.tex  +++ b/solving the sum.tex 
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&= a + \sum_{p = 2}^{\sqrt{n}}b + \sum_{p = 2}^{\sqrt{n}}\left[c\sum_{m = p}^{\frac{n}{p}} 1\right]\\  &= a + b\sum_{p = 2}^{\sqrt{n}}1 + c\sum_{p = 2}^{\sqrt{n}}\left[\sum_{m = p}^{\frac{n}{p}}\right]\\  &= a + b(\sqrt{n} - 1) + c\sum_{p=2}^{\sqrt{n}}[\frac{n}{p}-p+1]\\  &= a + b(\sqrt{n} - 1) + cn\sum_{p=2}^{\sqrt{n}}[\frac{1}{p}-p+1]\\ c\left(n\sum_{p=2}^{\sqrt{n}}[\frac{1}{p}]+\sum_{p=2}^{\sqrt{n}}[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)\\  &= a + b(\sqrt{n} - 1) + cn(H_{\sqrt{n}} - 1)\\  &= a - b + b\sqrt{n} + cnH_{\sqrt{n}} - cn