Mazdak Farrokhzad edited Version3.tex  over 10 years ago

Commit id: b060a79303695291b1e14e63ae5a717a25a298ab

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$$  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