JEE maths#6

Calculus Level 3

\[\large f(x) = (x-1)^{100}(x-2)^{2(99)}(x-3)^{3(98)} \cdots (x-100)^{100} \]

For \(f(x)\) as defined above, if \(k = \dfrac {f'(101)}{f(101)}\), find \(\dfrac k{50}-97\).


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