Question

[Trần Phương Thảo]

Lim \(\frac{2^n+3^n}{3-4\cdot3^{n+1}}\)

lim \(\frac{4^{n+1}+10^n}{3^n-4\cdot10^{n+1}}\)
lim \(\frac{3^n\cdot4^n-2^n}{12^n+5\cdot3^{n+2}}\)

lim \(\frac{\left(-2\right)^n+3^n}{\left(-2\right)^{n+1}-4\cdot3^{n+1}+2}\)

lim \(\frac{3^n-11}{1+7\cdot2^{n+1}}\)

lim \(\frac{2^n-3\cdot5^n+1}{3\cdot2^n+7\cdot4^{n+1}}\)

Answer 1

[Nguyễn Việt Lâm]

\(a=lim\frac{\left(\frac{2}{3}\right)^n+1}{3\left(\frac{1}{3}\right)^n-12}=-\frac{1}{12}\)

\(b=lim\frac{4\left(\frac{4}{10}\right)^n+1}{\left(\frac{3}{10}\right)^n-40}=-\frac{1}{40}\)

\(c=lim\frac{1-\left(\frac{2}{12}\right)^n}{1+45\left(\frac{3}{12}\right)^n}=\frac{1}{1}=1\)

\(d=\frac{\left(-\frac{2}{3}\right)^n+1}{-2\left(-\frac{2}{3}\right)^n-12+2\left(\frac{1}{3}\right)^n}=-\frac{1}{12}\)

\(e=\frac{1-11\left(\frac{1}{3}\right)^n}{\left(\frac{1}{3}\right)^n+14\left(\frac{2}{3}\right)^n}=\frac{1}{0}=+\infty\)

\(f=\frac{\left(\frac{2}{5}\right)^n-3+\left(\frac{1}{5}\right)^n}{3\left(\frac{2}{5}\right)^n+28\left(\frac{4}{5}\right)^n}=\frac{-3}{0}=-\infty\)