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Mazdak Farrokhzad edited Complexity analysis.tex
over 10 years ago
Commit id: b4a313e4f7847a11972b925b02daf72261cd38fd
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diff --git a/Complexity analysis.tex b/Complexity analysis.tex
index f78a55c..83bc0ec 100644
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\item $\displaystyle\sum_{n=s}^t f(n) + \sum_{n=s}^{t} g(n) = \sum_{n=s}^t \left[f(n) + g(n)\right]$
\item $\displaystyle\sum_{n=s}^t f(n) + \sum_{n=s}^{t} g(n) = \sum_{n=s}^t \left[f(n) + g(n)\right]$
\item $\displaystyle\sum_{i=m}^n 1 = n+1-m \therefore \sum_{i=m}^{n-1} 1 = n-m$
\item $\displaystyle\sum_{i=m}^n i = \frac{n(n+1)}{2} - \frac{m(m-1)}{2}
\therefore \sum_{i=m}^{n-1} i =
\frac{(n+1-m)(n+m)}{2}$ \frac{n(n-1)}{2} - \frac{m(m-1)}{2}$
\end{enumerate}