Don't run out of patience
Algebra
Level
5
\[ \large \sum _{r=1} ^n \dfrac{1}{r(r+1)(r+2)(r+3)} \]
If the closed form of the partial sum above can be expressed as \[\large \dfrac{1}{a} - \dfrac{1}{b(n+1)}+ \dfrac{1}{c(n+2)}- \dfrac{1}{d(n+3)} \; , \]
where \(a,b,c\) and \(d\) are constants, find \(a+b+c+d\).
by
Shanthanu Rai