To The End of The Line

Calculus Level 4

limnk=1nkn4+k4=ad ln(b+c) \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,da,b,c,d, with a,da,d coprime and bb square-free.

What is the value of a+b+c+da+b+c+d?

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