Question

lim стремиться к +бесконечности (4n-5/4n+1)^5n

Answer 1

$displaystyle lim_{n to infty}left(dfrac{4n-5}{4n+1}right)^{5n}=lim_{n to infty}left(1-dfrac{6}{4n+1}right)^{5ncdot frac{-6}{4n+1}cdot frac{4n+1}{-6}}=\ \ \ =e^{lim_{n to infty}-frac{30n}{4n+1}}=e^{-30/4}=e^{-15/2}$