Parameterized Finite Binomial Sums
Necdet Batır, Junesang Choi · Mathematics · 2024
We offer intriguing new insights into parameterized finite binomial sums, revealing elegant identities such as ∑k=0,k≠nm+n(−1)kn−km+nk=(−1)nm+nn(Hm−Hn), where n,m are non-negative integers and Hn is the harmonic number. These formulas beautifully capture the intricate relationship between harmonic numbers and binomial coefficients, providing a fresh and captivating perspective on combinatorial sums.