Question

Sa se determine a,b astfel incat:
a)$\lim_{n \to \infty} ( \frac{ an^{2} +bn+2}{bn^{2}+4n+3} )^{ \frac{ n^{2} }{n+1} } = \frac{1}{e}$
b)$\lim_{n \to \infty} ( \sqrt{ n^{2}+n+1 }- \sqrt{ n^{2}+an+2} ) ^{ \frac{b n^{2}+n }{n+1} } = \frac{1}{e}$
c)$\lim_{n \to \infty} (1+ \frac{ n^{2} +an+1}{n^{2}+3n-2} )^{n} = e$
d)$\lim_{n \to \infty} n( \sqrt[n]{a}- \sqrt[2n]{a} )=1 , a\ \textgreater \ 0$

Answer 1

Ti-am atasat solutia la a) ;)