Mazdak Farrokhzad edited Version2.tex  over 10 years ago

Commit id: b196a8ccf46c585f6ddbc1e4e0d5842b6e836f56

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$$  Substitute in $f_2$ with $f_1$ and simplify:  $$ \begin{equation}   \begin{split}  f_2(n) &  = b\sum_{j=i}^{n-1} 1 + c\sum_{j=i}^{n-1} (n-i) \\   &  = bn + cn\sum_{j=i}^{n-1} 1 - c\sum_{j=i}^{n-1} i =\\ \\   &  = bn + cn^2 - \frac{c}{2}n(n-1) = (c - \frac{c}{2})n^2 + (b + \frac{c}{2})n \\   &  = \frac{c}{2}n^2 + (b + \frac{c}{2})n $$ \end{split}   \end{equation}  Substitute in $T(n)$ with $f_2$  $$