deletions | additions       diff --git a/begin_claim_The_algorithm_runs__.tex b/begin_claim_The_algorithm_runs__.tex  index ec48f63..5ea4a14 100644  --- a/begin_claim_The_algorithm_runs__.tex  +++ b/begin_claim_The_algorithm_runs__.tex 
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We obtain the following after `unravelling' our recursive formula $i$ times:  \begin{align*}  R\left(n\right) &= &:=  O\left(n\right) + 2R\left(\frac{n}{2}\right)+ O\left(\log n\right)\\ &= iO\left(n\right) + 2^iR\left(\frac{n}{2^i}\right) + \sum_{j=0}^{i-1} 2^j O\left(\log \frac{n}{2^i}\right)  \end{align*}