# $$f(n)=\frac{1}{(x+n)(x+n+1)}$$

Algebra Level 2

$$f(n)=\frac{1}{(x+n)(x+n+1)}$$ for a positive integer $$n$$. If the following always holds regardless of the value of $$x$$, what is the sum of the constants $$a+b+c$$: $f(12)+f(13)+f(14)+\cdots+f(19)=\frac{c}{(x+a)(x+b)}?$

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