# Summation

Algebra Level 4

If $$\displaystyle\sum_{r=1}^n\dfrac{6r^3+18r^2+12r+2}{r(r+1)(r+2)}= \dfrac{an^3 +bn^2+cn}{2(n+d)(n+e)}$$

for positive integers $$a,b,c,d$$ and $$e$$, such that $$e >d$$

then evaluate $$\dfrac{2e(a+b)}{c+d}$$

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