# Dicey situation

I have a bias 6-sided dice (with faces 1, 2, 3, 4, 5, 6) such that for integer $$1\leq k \leq 6$$, the probability of rolling a $$k$$ is inversely proportional to $$k$$ itself. That is, $$P(k) \propto \dfrac1k$$. If the variance of the probability distribution of this dice can be expressed as $$\dfrac{V}{7^4}$$, find $$V$$.

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