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limn→∞∑k=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 ) n→∞limk=1∑nn4+k4k=da ln(b+c)
The above summation is fulfilled for positive integers a,b,c,da,b,c,da,b,c,d, with a,da,d a,d coprime and bbb square-free.
What is the value of a+b+c+da+b+c+da+b+c+d?
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