To The End of The Line

Calculus Level 4

\[ \displaystyle \lim_{n \to \infty} \sum_{k=1}^n \frac {k}{\sqrt{n^4+k^4}} = \frac {a}{d} \ \ln \left ( \sqrt b + c \right ) \]

The above summation is fulfilled for positive integers \(a,b,c,d\), with \(a,d \) coprime and \(b\) square-free.

What is the value of \(a+b+c+d\)?

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