Abel's Summation Formula

Definition

Abel’s Summation Formula for Natural Numbers

$\sum _{k=m}^n{a}_k{b}_k=a_n\sum _{k=m}^n{b}_k+\sum _{j=m}^{n-1}\left((a_j-a_{j+1})\sum _{k=m}^j{b}_k\right)$