[tex]3 \leq x+3 \leq 4 \\ \frac{1}{4} \leq \frac{1}{x+3} \leq \frac{1}{3} |* x^{n} \\ \frac{ x^{n} }{4} \leq \frac{ x^{n} }{x+3} \leq \frac{ x^{n} }{3} \\ [/tex]
Si integram intre 0 si 1.[tex]Obtinem: \frac{1}{4n+4} \leq \int\limits^1_0 { \frac{ x^{n} }{x+3} } \, dx \leq \frac{1}{3n+3} [/tex] Aplicand clestele se obtine ca sirul tinde la 0