Editorial for COCI '14 Contest 1 #1 Prosjek

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Let $S_k$ $S_{k}$ be the sum of the first $k$ $k$ numbers in sequence $A$ $A$ . It holds:

$\displaystyle B_k = \frac{S_k}{k}$ $B_{k} = \frac{S_{k}}{k}$

It follows:

$\displaystyle B_{k+1} = \frac{S_k+A_{k+1}}{k+1}$ $B_{k + 1} = \frac{S_{k} + A_{k + 1}}{k + 1}$

From here we get the expression for $A_{k+1}$ $A_{k + 1}$ :

$\displaystyle A_{k+1} = (k+1)B_{k+1}-S_k$ $A_{k + 1} = (k + 1) B_{k + 1} - S_{k}$

We calculate elements of the sequence $A_{k+1}$ $A_{k + 1}$ and their sum $S_k$ $S_{k}$ iteratively by using one loop over sequence $B$ $B$ .

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