aproximare de tip Stirling la derivata a doua

Moderators: Mihai Berbec, Liviu Paunescu

Post Reply
User avatar
Cezar Lupu
Site Admin
Posts: 612
Joined: Wed Sep 26, 2007 2:04 pm
Location: Bucuresti sau Constanta
Contact:
Contact Cezar Lupu

aproximare de tip Stirling la derivata a doua

Post by Cezar Lupu »

Sa se arate ca pentru orice \( n\geq 1 \) avem dubla inegalitate:

\( e^{1+\frac{n+1/2}{12(n+1)^3}}<\left(1+\frac{1}{n}\right)^{n+1/2}<e^{1+\frac{n+1/2}{12n^3}} \).
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
Top
Post Reply

Return to “Analiza reala”