Prove that:
$$\lim_{n\to1}-\frac{\zeta'(n)}{\zeta(n)^2}=1$$
I've checked on Mathematica and it's true, but I wanted to know how to derive such a result. L'Hospital didn't help.
2026-03-27 10:31:26.1774607486
Prove that $\lim_{n\to1}\,-\frac{\zeta'(n)}{\zeta(n)^2}=1$
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Hint: $$-\dfrac{\zeta'(z)}{\zeta(z)^2}=\left(\dfrac{1}{\zeta(z)}\right)'$$