\(\frac{1}{(x+k)(x+2k)}\)

Algebra Level 2

There exists a triple of integers \( (n, k, a) \) such that the following is an identity:

\[\begin{align} & \frac{1}{(x+k)(x+2k)}+\frac{1}{(x+2k)(x+3k)}+\cdots \\ &+ \frac{1}{(x+(n-1)k)(x+nk)} = \frac{6}{x^2+24x+a}? \end{align}\]

What is the value of \(a\)?

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