Tìm giới hạn của
[TEX]u_n= \frac{3^n-11}{1+5.2^n}[/TEX]
[TEX]u_n=\frac{2^(n+1)-3.5^n+3}{3.2^n+7.4^n}[/TEX]
[TEX]u_n=2.n-1+3^n[/TEX]
:-\" [TEX] lim \frac{3^n-11}{1+5.2^n} = lim \frac{1-\frac{1}{3^n}}{\frac{1}{3^n}+5.(\frac{2}{3})^n}[/TEX][TEX]= +\infty[/TEX]
:^o [TEX]lim \frac{2^{n+1}-3.5^n+3}{3.2^n+7.4^n}= lim \frac{\frac{2^{n+1}}{4^n}-3.(\frac{5}{4})^n+\frac{3}{4^n}}{3.\frac{2^n}{4^n}+7 =0 [/TEX]
=(( [TEX]lim (2n-1+3^n) = lim \frac{(2n+3^n)^2-1}{2n+3^n+1}[/TEX]
[TEX]= lim \frac{4n^2+4n.3^n+9^n-1}{2n+3^n+1}[/TEX]
[TEX]= lim \frac{4+\frac{4.3^n}{n}+\frac{9^n-1}{n^2}}{\frac{2}{n}+\frac{3^n}{n^2}+\frac{1}{n^2}}[/TEX]
[TEX]= +\infty[/TEX]