$$\lim_{n \to \infty}\left(n^{\operatorname{re}{\left(p\right)}} \left(n + 1\right)^{- \operatorname{re}{\left(p\right)}} \left|{\frac{\frac{\operatorname{atanh}{\left(g \right)}}{n^{3}} - \frac{1}{n^{3}}}{\frac{\operatorname{atanh}{\left(g \right)}}{\left(n + 1\right)^{3}} - \frac{1}{\left(n + 1\right)^{3}}}}\right|\right) = 1$$
$$\lim_{n \to 0^-}\left(n^{\operatorname{re}{\left(p\right)}} \left(n + 1\right)^{- \operatorname{re}{\left(p\right)}} \left|{\frac{\frac{\operatorname{atanh}{\left(g \right)}}{n^{3}} - \frac{1}{n^{3}}}{\frac{\operatorname{atanh}{\left(g \right)}}{\left(n + 1\right)^{3}} - \frac{1}{\left(n + 1\right)^{3}}}}\right|\right) = \infty$$
Más detalles con n→0 a la izquierda$$\lim_{n \to 0^+}\left(n^{\operatorname{re}{\left(p\right)}} \left(n + 1\right)^{- \operatorname{re}{\left(p\right)}} \left|{\frac{\frac{\operatorname{atanh}{\left(g \right)}}{n^{3}} - \frac{1}{n^{3}}}{\frac{\operatorname{atanh}{\left(g \right)}}{\left(n + 1\right)^{3}} - \frac{1}{\left(n + 1\right)^{3}}}}\right|\right) = \infty$$
Más detalles con n→0 a la derecha$$\lim_{n \to 1^-}\left(n^{\operatorname{re}{\left(p\right)}} \left(n + 1\right)^{- \operatorname{re}{\left(p\right)}} \left|{\frac{\frac{\operatorname{atanh}{\left(g \right)}}{n^{3}} - \frac{1}{n^{3}}}{\frac{\operatorname{atanh}{\left(g \right)}}{\left(n + 1\right)^{3}} - \frac{1}{\left(n + 1\right)^{3}}}}\right|\right) = \frac{8 \operatorname{atanh}{\left(g \right)} - 8}{e^{\log{\left(2 \right)} \operatorname{re}{\left(p\right)}} \operatorname{atanh}{\left(g \right)} - e^{\log{\left(2 \right)} \operatorname{re}{\left(p\right)}}}$$
Más detalles con n→1 a la izquierda$$\lim_{n \to 1^+}\left(n^{\operatorname{re}{\left(p\right)}} \left(n + 1\right)^{- \operatorname{re}{\left(p\right)}} \left|{\frac{\frac{\operatorname{atanh}{\left(g \right)}}{n^{3}} - \frac{1}{n^{3}}}{\frac{\operatorname{atanh}{\left(g \right)}}{\left(n + 1\right)^{3}} - \frac{1}{\left(n + 1\right)^{3}}}}\right|\right) = \frac{8 \operatorname{atanh}{\left(g \right)} - 8}{e^{\log{\left(2 \right)} \operatorname{re}{\left(p\right)}} \operatorname{atanh}{\left(g \right)} - e^{\log{\left(2 \right)} \operatorname{re}{\left(p\right)}}}$$
Más detalles con n→1 a la derecha$$\lim_{n \to -\infty}\left(n^{\operatorname{re}{\left(p\right)}} \left(n + 1\right)^{- \operatorname{re}{\left(p\right)}} \left|{\frac{\frac{\operatorname{atanh}{\left(g \right)}}{n^{3}} - \frac{1}{n^{3}}}{\frac{\operatorname{atanh}{\left(g \right)}}{\left(n + 1\right)^{3}} - \frac{1}{\left(n + 1\right)^{3}}}}\right|\right) = \infty$$
Más detalles con n→-oo