2.1.46 Calculation of limits
Condition: Calculate the limits: a) \( \lim _{n \rightarrow \infty} \frac{(n-1) !(n+2) !}{((n+3) !)^{2}} \) b) \( \lim _{n \rightarrow \infty} \frac{1+2+2^{2}+\cdots+2^{2 n}}{2^{2 n+3}} \) c) \( \lim _{n \rightarrow \infty} \frac{3^{n+1}+5^{n+2}}{\sqrt{6 \cdot 5^{2 n+1}+3}} \).
Calculation of various limits, using L'Hopital's rule, remarkable limits, power series, equivalent values of various other methods.