đặt a=\(\frac{\left(-1\right)^{n+3}.cos\left(pi.n^2+\frac{1}{n}+sinn\right)}{n\left(n-1\right)}\)
ta có; a<\(\frac{1}{n\left(n-1\right)}\)
=> lim \(\frac{1}{n\left(n-1\right)}\)=0
=> lima=0
tìm giới hanjn
1) lim \(\frac{\left(-1\right)^n}{n-3}\)
2) lim \(\frac{n\left(sin\left(pi.n^2\right)\right)}{n^2+3n-2}\)
tim giới hạn :
lim\(\frac{2n^3+3n^2-n+5}{\left(n^2+n+1\right)\left(n^2+2\right)}\)
tìm giới hạn:
lim\(\frac{n^2+2n-3}{n\left(n+1\right)}\)
Tính các giới hạn sau:
\(a.lim\left(\dfrac{\left(n-1\right)!+n!+3}{\left(n+2\right)!-\left(n-2\right)!}\right)\)
b.\(lim\left(\dfrac{2n+1}{n\cdot3^n}\right)\)
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 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) \(lim\left[\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{\left(2n-1\right)\left(2n+1\right)}\right]\)
Tìm giới hạn sau \(lim\dfrac{\left(3n+1\right)\left(1-8n\right)}{\sqrt[3]{n^3+3n-9}}\)
a; lim\(\frac{\sqrt{6n^4+n+1}}{2n^2+1}\)
b; lim \(\frac{\left(n+1\right)\left(2n+1\right)^2\left(3n+1\right)^3}{n^2\left(n+2\right)^2\left(1-3n\right)^2}\)