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Unformatted text preview: f; that is, assume l (f) £1 (f) = xHl + L k xHlkyk + L k xlkyk+l + yHl k=1 k=O = xHl + t. G)xHlkyk + t. (k ~ 1)xHlkyk + yHl = xHl + t. [ G) + (k ~ 1) ] xHlkyk + yHl by identity (5) HI = '"" (f + 1) Hlk k ~ k x y. k=O By the Principle of Mathematical Induction, the proof is complete. 19. (a) t, G) = G) + G) + G) + G) + (~) = 1 + 3 + 6 + 10 + 15 = 35 = G)' The sum here is the sum of the entries of Pascal's triangle on the third southwestnortheast diagonal (f) beginning with the entry above and to the left of 35 = G) and moving up and right....
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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