# But where to start from?

**Calculus**Level 5

\[\large\lim_{R\to\infty}\dfrac{1}{\displaystyle\prod_{I=5}^{R}\dfrac{(I-3)(I+4)}{\displaystyle\sum_{S=1}^I\dfrac{-2}{\dfrac1{S+2}+\dfrac1{S+1}-\displaystyle\sum_{H=S}^{\infty}\dfrac3{\displaystyle\sum_{A=1}^H\dfrac{2}{\displaystyle\sum_{B=A}^{\infty}\dfrac{1}{B^2+3B+2}}}}}}=\ ?\]