this is for holding javascript data
Mazdak Farrokhzad edited Version3.tex
over 10 years ago
Commit id: b060a79303695291b1e14e63ae5a717a25a298ab
deletions | additions
diff --git a/Version3.tex b/Version3.tex
index e5171b4..89f98cd 100644
--- a/Version3.tex
+++ b/Version3.tex
...
$$
f_2(n,i) =
\sum_{j=i}^{n-1} (c + f_1(j,i))
=\\ =
c\sum_{j=i}^{n-1} 1 + d\sum_{j=i}^{n-1} 1 + d\sum_{j=i}^{n-1} j - di\sum_{j=i}^{n-1} 1 =\\
(c + d)\sum_{j=i}^{n-1} 1 + d(\frac{n(n-1)}{2} - \frac{i(i-1)}{2}) - di(n-i) =\\
(c + d)\sum_{j=i}^{n-1} 1 + \frac{d}{2}n(n-1) + \frac{d}{2}i^2 + \frac{d}{2}(1-2n)i