AMC 10 2025 Part B Problem 15

The sum \displaystyle\sum_{k=1}^{\infty}\frac{1}{k^3+6k^2+8k} can be expressed as \dfrac{a}{b}, where a and b are relatively prime positive integers. What is a+b?

Answer Choices:

A. 89

B. 97

C. 102

D. 107

E. 129