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a theorem in graph theory.. please help

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electroboy

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how does the rounded step came in the image below??? please help..

 

eagle5

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The maximum value of

\[\sum_{i=1}^{k} n_i^2\]

is obtained for:

\[n_1 =n-k+1, \quad\quad n_i = 1,\quad i=2..k\].

If you put the numbers you get that value.
 

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