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Suppose that p and q are integers with 0 < p, 0

Suppose that p and q are integers with 0 < p, 0

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.2: Arithmetic Sequences And Partial Sums
Problem 6ECP: Find the sum of the integers (a) from 1 to 35 and (b) from 1 to 2N.
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Suppose that p and q are integers with 0 < p, 0 <p+q, and the greatest common divisor of p and q is 1. For a positive integer k, let P(k) be the lowest common multiple of p+q, p+2q,p+ 3q,,p+kq. Prove that 1 P(k) 1 k lim log k→∞ = Σ o(1) m 1<m<l where (a) (1) is the number of integers between 1 and 1 that are relatively prime to 1 and (b) the greatest common divisor of m and 1 is 1 for all m.
Transcribed Image Text:Suppose that p and q are integers with 0 < p, 0 <p+q, and the greatest common divisor of p and q is 1. For a positive integer k, let P(k) be the lowest common multiple of p+q, p+2q,p+ 3q,,p+kq. Prove that 1 P(k) 1 k lim log k→∞ = Σ o(1) m 1<m<l where (a) (1) is the number of integers between 1 and 1 that are relatively prime to 1 and (b) the greatest common divisor of m and 1 is 1 for all m.
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