deletions | additions       diff --git a/solving the sum.tex b/solving the sum.tex  index c96b575..eec1419 100644  --- a/solving the sum.tex  +++ b/solving the sum.tex 
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We know that $H_n$ is bounded from above by a constant multiple of $\log(n)$, meaning $H_n \in \mathcal{O}(\log(n))$\\  Thus: \[T(n) \in \mathcal{O}(nlog(\sqrt{n}))\]  We use the logarithm identity $log_b(x^d) = dlog_b(x)$ to simplify and yield: simplify, which gives us:  \[T(n) \in \mathcal{O}(nlog(n))\]