Solved: Determine a formula involving binomial

Chapter 5, Problem 5.4.39

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Determine a formula involving binomial coefficients for the nth term of a sequence if its initial terms are those listed. [Hint: Looking at Pascal's triangle will be helpful. Although infinitely many sequences start with a specified set of terms, each of the following lists is the start of a sequence of the type desired.] a) 1 , 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, .. . b) 1 , 4, 10, 20, 35, 56, 84, 120, 165, 220, .. . c) 1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620, ... d) 1, 1, 2, 3, 6, 10, 20, 35, 70, 126, ... e) 1, 1, 1, 3, 1 , 5, 15, 35, 1, 9, ... t) 1, 3, 15, 84, 495, 3003, 18564, 1 16280, 735471, 4686825, ...

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