Ta có: \(1+2+3+...+2n=\dfrac{2n\left(2n+1\right)}{2}=n\left(2n+1\right)=2n^2+n\)
\(\Rightarrow\lim\limits\dfrac{1+2+3+...+2n}{2n^2}=\lim\limits\dfrac{2n^2+n}{2n^2}\\ =\lim\limits\left(1+\dfrac{1}{2n}\right)=1\).
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) \(lim\dfrac{2n^3+n^2-3n+1}{2-3n}\)
Tìm các giới hạn sau:
\(a,lim\dfrac{2n^2+1}{3n^3-3n+3}\)
\(b,lim\dfrac{-3n^3+1}{2n+5}\)
\(c,lim\dfrac{n^3-2n+1}{-3n-4}\)
Tìm các giới hạn sau:
\(a,lim\dfrac{2n+1}{-3n+2}\)
\(b,lim\dfrac{5n^3-2n+1}{n-2n^3}\)
đặt \(a=lim\dfrac{3n^3-2n+1}{4n^4+2n+1}\). tìm \(lim\dfrac{an^3-\left(a+2\right)n^2+1}{4an^3-n^2+3n+3}\)
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 \(\left(\sqrt{n^2+3n-1}-\sqrt[3]{n^3-n}\right)\)
Tính :6/ lim\(\dfrac{-n^2+2n+1}{\sqrt{3n^4+2}}\)
7/ lim \(\dfrac{\sqrt{n^3-2n+5}}{3+5n}\)
10/ lim\(\dfrac{1+3+5+...+\left(2n+1\right)}{3n^3+4}\)
tìm giới hạn L= lim \(\dfrac{1-2+3-4+...+\left(2n-1\right)-2n}{2n+1}\)
tìm
\(lim\left(2n-1\right)\sqrt{\dfrac{2n+3}{n^4-n^2+2}}\)
Tìm các giới hạn sau
\(a,lim\left(\sqrt{n^2+n+1}-n\right)\)
\(b,lim\dfrac{\sqrt{n^3+2n}-2n^2}{3n+1}\)
