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Next: Useful Series Up: CSE 2320: Algorithms and Previous: Example: Generate and Test

Summations


\begin{eqnarray*}\sum_{k=1}^n a_k & = & a_1 + a_2 + \ldots + a_n \\
& = & 0 \; {\rm if} \; n = 0
\end{eqnarray*}


Linearity


\begin{displaymath}\sum_{k=1}^n (c a_k + b_k) = c \sum_{k=1}^n a_k + \sum_{k=1}^n b_k \end{displaymath}


\begin{displaymath}\sum_{k=1}^n \Theta(f(k)) = \Theta(\sum_{k=1}^n f(k)) \end{displaymath}

(applies to k) $\;\;\;\;\;$(applies to n)



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