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Unformatted text preview: n is the sum of exactly k rolls of a die is the coeï¬€ecient of x n in the generating function ( x + x 2 + Â·Â·Â· + x 6 ) k . Now, we can achieve n as a sum in 0 rolls, 1 roll, 2 rolls, etc., i.e., when k = 0 , 1 , 2 ,... Therefore, the total number of ways in which we can obtain n as the sum is the coeï¬€ecient of x n in the generating function âˆž X k =0 ( x + x 2 + Â·Â·Â· + x 6 ) k = 1 1xx 2Â·Â·Â·x 6 . Section 8.5 8. 270649458 + 26 + 28 + 2214 = 116. 12. 31 + 103 = 38. 2...
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 Fall '12
 Gupta
 Math, Summation, Generating function

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