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I'm working on a discrete math exercise and need an explanation and answer to help me learn.
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Generating Functions and Number theory:
1. A sequence is defined as S(0) = 1, and S(k) = S(k – 1) + k, for k >= 1. Find the generating function for S(k), and
give the kth term.
2. What is the sequence for the generating function 1(1−𝑥)^2.
3. Let p > 2 be a prime. Prove that p divides the sum of any consecutive p integers.
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