Câu 1: Tính: lim ( \(\frac{sin5n}{3n}\) -2 )
Câu 2: Tính: lim ( 5- \(\frac{n^2cos2n}{n^2+1}\) )
Câu 3: Tính: lim \(\frac{\frac{1}{2}+1+\frac{3}{2}+...+\frac{n}{2}}{n^2+1}\)
Câu 4: Tính tổng của cấp số nhân lùi vô hạn: \(\frac{1}{2}\) ; \(\frac{-1}{4}\); \(\frac{1}{8}\);...; \(\frac{\left(-1\right)^{n+1}}{2^n}\);...
Câu 5: Tính: lim \(\frac{n-2\sqrt{n}sin2x}{2n}\)
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\(\frac{1^2+2^2+3^2+.....+n^2}{n\left(n+1\right)\left(n+2\right)}\)
tính giới hạn sau
a, lim\(\frac{1}{\sqrt{n+2}-\sqrt{n+1}}\)
b, lim\(\frac{8^{2n+3}-3^{3n+2}}{4^{3n+4}+5^{2n+3}}\)
tính tổng CSN: \(1,-\frac{1}{2},\frac{1}{4},-\frac{1}{8},...,\left(-\frac{1}{2}\right)^{n-1},...\)
tính tổng S= \(1+0,9+\left(0,9\right)^2+\left(0,9\right)^3+...+\left(0,9\right)^{n-1}+...\)
\(lim\left(\sqrt[3]{n-n^3}+\sqrt{n^2+3n}\right)\)
\(lim\left(\sqrt{n-2\sqrt{n}}-\sqrt{n+4}\right)\)
\(lim\left(\sqrt[3]{3n^2+n^3}-n\right)\)
\(lim\left(\sqrt[3]{n^3+6n}-\sqrt{n^2-4n}\right)\)
\(lim\frac{-3^{n+1}+4^{n+1}}{5.3^n+3.2^{2n-1}}\)
\(lim\left(\frac{3^{2n}-5^{n+1}+7^{n+1}}{3^{n+2}+5^n+2^{3n+2}}\right)\)
\(lim\left(\frac{6^{n+1}+3^{2n+5}}{3^{2n+3}-2^{2n-1}}\right)\)
a) \(lim\frac{\left(-2\right)^n+3^n}{\left(-2\right)^{n+1}+3^{n+1}}\)
b) \(lim\frac{\left(2n-1\right)\left(n+1\right)\left(3n+4\right)}{\left(5-6n\right)^3}\)
c) \(lim\left(\sqrt{n^2+5n+1}-\sqrt{n^2-2}\right)\)
d) \(lim\frac{5\cdot3^n-6^{n+1}}{4\cdot2^n+6^n}\)
e) \(lim\left(-2n^3-3n^2+5n-2020\right)\)
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 \(\sqrt{\frac{cos2n}{3n}+9}\)
P2= lim\(\frac{\sqrt{n+1}}{\sqrt{n}+1}\)
M1= lim\(\frac{1+2+3+...+n}{^{ }n^2+2}\)
A5= lim\(\frac{\left(4-2n\right)^3\left(7n^2+1\right)^5}{\left(n^4+n^3-1\right)^2\left(4-5^5\right)}\)
5/ lim \(\frac{\left(12-n\right)^3\left(n-2\right)}{\sqrt{n^8-1}-2n^4}\)
6/ lim \(\frac{\sqrt[3]{3-8n^3}-n}{2n+5}\)
7/ lim \(\frac{\sqrt{n^6-2n+1}}{\sqrt{4n^6+3n}}\)
8/ lim \(\left(n^4+2n-20\right)\)
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 \(\frac{\left(3-2n\right)^4}{\left(n+1\right)^2\left(n^2+1\right)}\)
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 \(\left(u_n+v_n\right)\)