Abstract
The sum of the telescoping series formed by reciprocals of the cubic polynomials with three different negative integer roots
Highlights
K=1 converges to a limit s if and only if the sequence of partial sums sn = a1 + a2 + ⋯ + an converges to s, i.e. lim sn = s
Representing the telescoping series formed by reciprocals of the cubic polynomials with negative roots k = −2, k = −6, and k = −9
Before we derive the main result of this paper, we present two lemmas
Summary
K=1 converges to a limit s if and only if the sequence of partial sums sn = a1 + a2 + ⋯ + an converges to s, i.e. lim sn = s. The sum of the reciprocals of some positive integers is generally the sum of unit fractions. K=1 has the general kth term, after partial fraction decomposition, in a form ak = After that we arrange the terms of the nth partial sum sn = a1 + a2 + ⋯ + an in a form where can be seen what is cancelling.
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