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show this inequality with $\frac{d^i}{dx^i}\left(1-\left(\frac{-x}{\ln(1-x)}\right)^{1/K}\right) \Bigg|_{x=0}>0, ~~~\forall i\in N^{+}$
I am trying to solve this Komal problem 661:
Let $K$ be a fixed positive integer. Let $(a_{0},a_{1},\cdots )$ be the sequence of real numbers that satisfies $a_{0}=-1$ and
$$\sum_{i_{0},i_{1},\cdots,...
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