1, \(lim\frac{3}{n-2}=lim\frac{n\frac{3}{n}}{n\left(1-\frac{2}{n}\right)}=0\)
2, \(lim\frac{n-1}{n-2}=lim\frac{n\left(1-\frac{1}{n}\right)}{n\left(1-\frac{2}{n}\right)}=1\)
3, \(lim\frac{7n^2-3}{n^2-2}=lim\frac{n^2\left(7-\frac{3}{n^2}\right)}{n^2\left(1-\frac{2}{n^2}\right)}=7\)
P2= lim\(\frac{\sqrt{n+1}}{\sqrt{n}+1}\)
M1= lim\(\frac{1+2+3+...+n}{^{ }n^2+2}\)
A5= lim\(\frac{\left(4-2n\right)^3\left(7n^2+1\right)^5}{\left(n^4+n^3-1\right)^2\left(4-5^5\right)}\)
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 \(\frac{2^n-3\cdot5^n+1}{3\cdot2^n+7\cdot4^{n+1}}\)
tìm các giới hạn
a)lim(\(\sqrt{n+1}-\sqrt{n}\))
b)lim\(\left(\sqrt{n+5n+1}-\sqrt{n^2-n}\right)\)
c)lim\(\left(\sqrt{3n^2+2n-1}-\sqrt{3n^2-4n+8}\right)\)
d)lim\(\frac{2^n+6^n-4^{n+1}}{3^n+6^{n+1}}\)
e)lim\(\frac{3^n-4^n+5^n}{3^n+4^n-5^n}\)
f)lim\(\frac{1+3+5+.....+\left(2n+1\right)}{3n^2+4}\)
g)lim[\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{n\left(n+1\right)}\)]
h)lim\(\frac{1^2+2^2+3^2+.....+n^2}{n\left(n+1\right)\left(n+2\right)}\)
1/ lim \(\frac{n^2-2n}{n^2-n+6}\)
2/ lim \(\frac{4n^2-6}{n^4+n^2-17}\)
3/ lim \(\frac{n^3-n^2+n}{n+7}\)
4/ lim \(\frac{\left(3-2n\right)^4}{\left(n+1\right)^2\left(n^2+1\right)}\)
\(lim\left(\sqrt[3]{n-n^3}+\sqrt{n^2+3n}\right)\)
\(lim\left(\sqrt{n-2\sqrt{n}}-\sqrt{n+4}\right)\)
\(lim\left(\sqrt[3]{3n^2+n^3}-n\right)\)
\(lim\left(\sqrt[3]{n^3+6n}-\sqrt{n^2-4n}\right)\)
\(lim\frac{-3^{n+1}+4^{n+1}}{5.3^n+3.2^{2n-1}}\)
\(lim\left(\frac{3^{2n}-5^{n+1}+7^{n+1}}{3^{n+2}+5^n+2^{3n+2}}\right)\)
\(lim\left(\frac{6^{n+1}+3^{2n+5}}{3^{2n+3}-2^{2n-1}}\right)\)
tính các giới hạn sau:
a, lim\(\frac{3.2^n-8.7^n}{4.3^n+5.7^n}\)
b, lim\(\frac{2^{n+1}\left(3.2^n-3^{n-2}\right)}{3^n\left(2^{n-1}+4\right)}\)
c, lim\(\frac{\left(-3\right)^n+2.5^n}{1-5^n}\)
d, lim\(\frac{1+2+3+...+n}{n^2+n+1}\)
12/ lim\(\frac{3^n+5^{n+2}}{2.4^n+5^n}\)
13/ lim\(\left(\sqrt{n^4+3n+1}-n^2-1\right)\)
14/ lim\(\left(\sqrt[3]{n^2-n^3}+n\right)\)
15/ lim\(\frac{n^2+\sqrt[3]{1-n^6}}{\sqrt{n^4+1}-n^2}\)
Tính:
Câu 1: lim ( \(\frac{1}{\sqrt{n^2+1}}\) + \(\frac{1}{\sqrt{n^2+2}}\) + ... + \(\frac{1}{\sqrt{n^2+n}}\) )
Câu 2: lim ( \(\frac{1}{1.2}\) + \(\frac{1}{2.3}\) +...+ \(\frac{1}{n\left(n+1\right)}\) )
Câu 3: lim ( \(\frac{1}{n^2}\) + \(\frac{3}{n^2}\) + \(\frac{5}{n^2}\) +...+ \(\frac{2n-1}{n^2}\) )
Câu 4: lim ( \(\sqrt{3+\frac{n^2-1}{3+n^2}}\) - \(\frac{\left(-1\right)^n}{2^n}\) )
Câu 5: lim \(\sqrt{\frac{cos2n}{3n}+9}\)
Câu 1: lim \(\frac{1^3+2^3+...+n^3}{n\left(n^3+1\right)}\)
Câu 2: lim (\(4+\frac{\left(-1\right)^n}{n+1}\) )
Câu 3: lim\(\sqrt{9-\frac{cos2n}{n}}\)
Câu 4: lim ( \(n^2sin\frac{n\pi}{5}-2n^3\))
Câu 5: Cho \(u_n=\frac{\left(-1\right)^n}{n^2+1}\) và \(v_n=\frac{1}{n^2+2}\). Khi đó tính lim \(\left(u_n+v_n\right)\)