AMC 10B 2025 (Problem 15)

The sum

\sum_{k=1}^{\infty}\frac{1}{k^3+6k^2+8k}

can be expressed as

\frac{a}{b}

, where

a

and

b

are relatively prime positive integers. What is

a+b

\text{(A)}\;89

\text{(B)}\;97

\text{(C)}\;102

\text{(D)}\;107

\text{(E)}\;129