Discrete integration-by-parts: Σ a_n b_n = A_N b_N − Σ A_n (b_{n+1} − b_n), A_n the partial sums of a. Abel 1826. Tool for Dirichlet series bounds: if A_n = O(1) and b_n ↓ 0 then Σ a_n b_n converges (Dirichlet test). Used in the proofs…
Discrete integration-by-parts: Σ a_n b_n = A_N b_N − Σ A_n (b_{n+1} − b_n), A_n the partial sums of a. Abel 1826. Tool for Dirichlet series bounds: if A_n = O(1) and b_n ↓ 0 then Σ a_n b_n converges (Dirichlet test). Used in the proofs…