this is for holding javascript data
Mazdak Farrokhzad edited Version2.tex
over 10 years ago
Commit id: b196a8ccf46c585f6ddbc1e4e0d5842b6e836f56
deletions | additions
diff --git a/Version2.tex b/Version2.tex
index 465ce43..384fa86 100644
--- a/Version2.tex
+++ b/Version2.tex
...
$$
Substitute in $f_2$ with $f_1$ and simplify:
$$ \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
$$ \end{split}
\end{equation}
Substitute in $T(n)$ with $f_2$
$$