[math-fun] Question about summation of 1/P(n) where P(x) is an integer polynomial
14 Feb
2021
14 Feb
'21
2:28 p.m.
Suppose P(x) is a polynomial with integer coefficients. Assume that no positive integer is a root of P(x). Is it possible that Sum 1/P(n) = 1 where n = 1, 2, 3, ..., runs through the positive integers? —Dan
14 Feb
14 Feb
2:54 p.m.
1/(n*(n+1)) = 1/n - 1/(n+1) sum(1/(n*(n+1)), n=1..inf) = sum(1/n - 1/(n+1), n=1..inf) = 1 -- Gene On Sunday, February 14, 2021, 1:28:53 PM PST, Dan Asimov <asimov@msri.org> wrote: Suppose P(x) is a polynomial with integer coefficients. Assume that no positive integer is a root of P(x). Is it possible that Sum 1/P(n) = 1 where n = 1, 2, 3, ..., runs through the positive integers? —Dan
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Eugene Salamin