\(=\lim\left(\dfrac{1+2+...+n-1}{n^2}\right)=\lim\dfrac{n\left(n-1\right)}{2n^2}=\dfrac{1}{2}\)
Tìm các giới hạn sau:
a)\(lim\left[n^2\left(\sqrt{n^2+2}-\sqrt{n^2+4}\right)\right]\)
b)lim( \(\dfrac{3}{n-2}-5n\))
c) lim(\(\dfrac{n-1}{\sqrt{3}-n}-\dfrac{4}{2^{-n}}\))
d) \(lim\left(\dfrac{n^2-4}{n-2}-\dfrac{3n^2+4}{n}\right)\)
e) \(lim\dfrac{\sqrt{n^2+1}-n\sqrt{5}}{\sqrt{n^2+1}+n\sqrt{5}}\)
giá trị của giới hạn lim \(\dfrac{\dfrac{1}{2}+1+\dfrac{3}{2}+...+\dfrac{n}{2}}{n^2+1}\)
Tìm các giới hạn sau:
a) \(lim\sqrt[3]{-n^3+2n^2-5}\)
b) \(lim\dfrac{1}{\sqrt{n+1}-\sqrt{n}}\)
c) \(lim\left(\dfrac{1}{n+1}-n\right)\)
d) \(lim\left(\dfrac{2n^2-1}{n+1}-2n\right)\)
e) \(lim\dfrac{2n^3+n^2-3n+1}{2-3n}\)
a,CMR :dãy u(n)=\(\left(1+\dfrac{1}{n}\right)^n\)có giới hạ hữu hạn
b đặt lim(1+\(\dfrac{1}{n}\))^n =e .Tính các giưới hạn sau ; lim\(\left(\dfrac{n+1}{n-1}\right)^{n+2}\)và lim\(\left(\dfrac{n-2}{n+3}\right)^{n+1}\)
Tính giới hạn sau lim\(\dfrac{1+\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2+...+\left(\dfrac{1}{3}\right)^n}{1+\dfrac{2}{5}+\left(\dfrac{2}{5}\right)^2+...+\left(\dfrac{2}{5}\right)^n}\)
Tính các giới hạn sau
1,Lim\(\left(\dfrac{2n^3}{2n^2+3}+\dfrac{1-5n^2}{5n+1}\right)\)
2,a,Lim\(\left(\sqrt{n^2+n}-\sqrt{n^2+2}\right)\)
b,Lim\(\dfrac{\sqrt{n^4+3n-2}}{2n^2-n+3}\)
c,Lim\(\dfrac{\sqrt{n^2-4n}-\sqrt{4n^2+1}}{\sqrt{3n^2+1}-n}\)
Tìm các giới hạn sau:
\(a,lim\dfrac{3+4^n}{1+3.4^{n+1}}\)
\(b,lim\dfrac{\left(-2\right)^n+3^n}{\left(-2\right)^{n+1}+3^{n+1}}\)
tính các giới hạn sau:
a) lim (3n2+n2-1)
b)lim \(\dfrac{n^3+3n+1}{2n-n^3}\)
c) lim \(\dfrac{-2n^3+3n+1}{n-n^2}\)
d) lim \(\left(n+\sqrt{n^2-2n}\right)\)
e) lim \(\left(2n-3.2^n+1\right)\)
f) lim \(\left(\sqrt{4n^2-n}-2n\right)\)
g) lim \(\left(\sqrt{n^2+3n-1}-\sqrt[3]{n^3-n}\right)\)
giới hạn \(lim\dfrac{1-2+4-...+\left(-2\right)^{n-1}}{1-3+9-...+\left(-3\right)^{n-1}}=\dfrac{4\left[1-\left(-2\right)^n\right]}{3\left[1-\left(-3\right)^n\right]}\) bằng?
