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\[\Lim_{n\to \infty } \left( \frac{n-26}{n+1} \right)^{26n}\]

\[\left( \frac{n-26}{n+1} \right)^{26n}=\left(\frac{(n+1)-27}{n+1}\right)^{26n}=\frac{\left[\left(1-\frac{27}{n+1}\right)^{n+1}\right]^{26}}{\left(1-\frac{27}{n+1}\right)^{26}}\longrightarrow\frac{\left(e^{-27}\right)^{26}}{1}=e^{-702}\]