Derivative Magic II

Calculus Level 5

Define $$f(x)=\displaystyle\sum_{k=1}^{2016} \dfrac{x^{k+1}}{k+1}$$ . If $$f^{(2016)} (100)$$ can be evaluated as $$a\times b!$$ where $$b$$ is maximum, find $$a+b$$ .

Bonus: If $$f(x)=\displaystyle\sum_{k=1}^{n} \dfrac{x^{k+1}}{k+1}$$ , find $$f^{(n)} (x)$$ .

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