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Define f(x)=∑k=11001xk+1kf(x)=\displaystyle\sum_{k=1}^{1001} \dfrac{x^{k+1}}{k}f(x)=k=1∑1001kxk+1 . If f(1001)(100)f^{(1001)} (100)f(1001)(100) can be evaluated as a×b!a\times b!a×b! where bbb is maximum, find a+ba+ba+b .
Bonus: If f(x)=∑k=1nxk+1kf(x)=\displaystyle\sum_{k=1}^{n} \dfrac{x^{k+1}}{k}f(x)=k=1∑nkxk+1 , find f(n)(x)f^{(n)} (x)f(n)(x) .
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