aproximare de tip Stirling la derivata a doua
Posted: Thu Feb 04, 2010 11:53 pm
Sa se arate ca pentru orice \( n\geq 1 \) avem dubla inegalitate:
\( e^{1+\frac{n+1/2}{12(n+1)^3}}<\left(1+\frac{1}{n}\right)^{n+1/2}<e^{1+\frac{n+1/2}{12n^3}} \).
\( e^{1+\frac{n+1/2}{12(n+1)^3}}<\left(1+\frac{1}{n}\right)^{n+1/2}<e^{1+\frac{n+1/2}{12n^3}} \).