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Unformatted text preview: ··· + n = ( n-m + 1)( n + m ) 2 Geometric series: n X k =0 x k = 1 + x + + x 2 ··· + x n = x n +1-1 x-1 x 6 = 1 ∞ X k =0 x k = 1 1-x | x | < 1 Recurrences. “AMT: Ambitious Master Theorem”: T ( n ) = ± aT ( n/b ) + cn d n > 1 f n = 1 implies T ( n ) = ² f + c ab-d-1 ³ n log b a-( cn d ab-d-1 ) = ± Θ( n log b a ) a > b d Θ( n d ) a < b d n d ( f + c log b n ) = Θ( n d log b n ) a = b d . Miscelleneous. Stirling’s Approximation: n ! ≥ √ 2 πn ² n e ³ n 2...
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This note was uploaded on 01/13/2012 for the course CMSC 351 taught by Professor Staff during the Fall '11 term at University of Louisville.
- Fall '11