What
Close Σ_{k=a}^{b} p(k)/q(k) for polynomial p, q by partial fraction decomposition followed by telescoping and evaluation via ψ(b+1) - ψ(a) (digamma). Handles sums that Gosper misses because the ratio is not hypergeometric.
Applications
Exact values of series like Σ 1/(k²+k) = 1, Σ 1/(k(k+1)(k+2)), sums arising in combinatorics and analysis.
Notes
Alkahest's sum_indefinite uses Gosper only; rational-function sums that are not hypergeometric terms fall through.
Tracked from mathematical coverage gap analysis.
What
Close
Σ_{k=a}^{b} p(k)/q(k)for polynomialp,qby partial fraction decomposition followed by telescoping and evaluation viaψ(b+1) - ψ(a)(digamma). Handles sums that Gosper misses because the ratio is not hypergeometric.Applications
Exact values of series like
Σ 1/(k²+k) = 1,Σ 1/(k(k+1)(k+2)), sums arising in combinatorics and analysis.Notes
Alkahest's
sum_indefiniteuses Gosper only; rational-function sums that are not hypergeometric terms fall through.Tracked from mathematical coverage gap analysis.