lim(n2+n+1)= lim \(\frac{n^2}{n^2}+\frac{1}{n}+\frac{1}{n^2}\)=1
lim(n2+n+1)= lim \(\frac{n^2}{n^2}+\frac{1}{n}+\frac{1}{n^2}\)=1
Tìm giới hạn các dãy số sau
a) \(lim\dfrac{2^n+6^n-4^{n-1}}{3^n+6^{n+1}}\)
b) \(lim\dfrac{1+3+5+...+\left(2n+1\right)}{3n^2+4}\)
c) \(lim\dfrac{1+2+3+...+n}{n^2-3}\)
d) \(lim\left[\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{n\left(n+1\right)}\right]\)
e) \(lim\left[\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{\left(2n-1\right)\left(2n+1\right)}\right]\)
Bài 1. Tìm các giới hạn sau:
a) \(\lim\limits\dfrac{-2n+1}{n}\)
b) \(\lim\limits_{x\rightarrow1}\dfrac{3-\sqrt{x+8}}{x-1}\)
Tìm giới hạn dãy số sau
\(lim\dfrac{\left(2n-1\right)\left(3n^2+2\right)^3}{-2n^5+4n^3-1}\)
\(lim\left(3.2^{n+1}-5.3^n+7n\right)\)
Tìm a,b để:
1, Lim(\(\sqrt{4n^2+2n+1}\)-an+b)=1
2, Lim( \(\sqrt{n^2+6n-1}-\sqrt{an^2+bn+2}\))=4
Tìm lim \(\dfrac{3}{\sqrt{n+1}-\sqrt{n+3}}\)
a, lim \(\dfrac{\sqrt{n+1}}{1+\sqrt{n}}\)
b, lim \(\dfrac{1+2+...+n}{n^2+2}\)
c, lim \((\sqrt{n^2+n+1}-n)\)
d, lim \((\sqrt{3n-1}-\sqrt{2n-1})\)
e, lim \((\sqrt[3]{n^3+2n^2}-n)\)
g, lim \(\dfrac{(2)^{n}+(3)^{n+2}}{4×(3)^{n}+(2)^{n+3}}\)
tìm giới hanjn
1) lim \(\frac{\left(-1\right)^n}{n-3}\)
2) lim \(\frac{n\left(sin\left(pi.n^2\right)\right)}{n^2+3n-2}\)
tìm giá trị giới hạn \(lim\dfrac{n\sqrt{n}+1}{n^2+2}\)
\(u_n=\dfrac{n}{1+n^2+n^4}\). Tìm \(\lim\limits_{\left(u_1+u_2+...+u_n\right)}\)