Derivative Magic II

Calculus Level 5

Define f(x)=k=12016xk+1k+1f(x)=\displaystyle\sum_{k=1}^{2016} \dfrac{x^{k+1}}{k+1} . If f(2016)(100)f^{(2016)} (100) can be evaluated as a×b!a\times b! where bb is maximum, find a+ba+b .

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

Try Part I
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