Mazdak Farrokhzad edited Complexity analysis.tex  over 10 years ago

Commit id: b4a313e4f7847a11972b925b02daf72261cd38fd

deletions | additions      

       

\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}