Second-order upper bound on the Bernoulli relative entropy: $d(p,q) \le \frac{(q-p)^2}{p\,(2-p-q)}$ when $p < q$ and $p + q \le 1$

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Second-order upper bound on the Bernoulli relative entropy: $d(p,q) \le \frac{(q-p)^2}{p\,(2-p-q)}$ when $p < q$ and $p + q \le 1$ · Prove2Me