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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