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**Unformatted text preview: **n is the sum of exactly k rolls of a die is the coeﬀecient of x n in the generating function ( x + x 2 + ··· + 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 coeﬀecient of x n in the generating function ∞ X k =0 ( x + x 2 + ··· + x 6 ) k = 1 1-x-x 2-···-x 6 . Section 8.5 8. 270-64-94-58 + 26 + 28 + 22-14 = 116. 12. 31 + 10-3 = 38. 2...

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- Fall '12
- Gupta
- Math, Summation, Generating function