\(=\lim\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{n}-\dfrac{1}{n+1}\right)\)
\(=\lim\left(1-\dfrac{1}{n+1}\right)=1\)
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Bài 1: Giới hạn của dãy số
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Tính \(lim\dfrac{1+\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2+...+\left(\dfrac{1}{3}\right)^n}{1+\dfrac{2}{5}+\left(\dfrac{2}{5}\right)^2+...+\left(\dfrac{2}{5}\right)^n}\)
Tính giới hạn sau lim\(\dfrac{1+\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2+...+\left(\dfrac{1}{3}\right)^n}{1+\dfrac{2}{5}+\left(\dfrac{2}{5}\right)^2+...+\left(\dfrac{2}{5}\right)^n}\)
1. lim\(\dfrac{\left(n+2\right)^{50}.\left(n-3\right)^{80}}{\left(2n-1\right)^{40}.\left(3n-2\right)^{45}}\)
2. lim\(\dfrac{4^n}{2.3^n+4^n}\)
3. lim\(\dfrac{3^n-2.5^n}{7+3.5^n}\)
4. lim\(\dfrac{4^n-5^n}{2^{2n}+3.5^{2n}}\)
5. lim\(\dfrac{\left(-3\right)^n+5^n}{2.\left(-4\right)^n+5^n}\)
Cho dãy xác định \(\left\{{}\begin{matrix}u\left(1\right)=\dfrac{1}{4}\\u\left(n+1\right)=\left(u\left(n\right)\right)^2+\dfrac{u\left(n\right)}{2}\end{matrix}\right.\)
CM với mọi n thì 0<u(n)<\(\dfrac{1}{4}\) và\(\dfrac{u\left(n+1\right)}{u\left(n\right)}\le\dfrac{3}{4}\)
Từ đó suy ra limu(n)=o
Cho dãy xác định \(\left\{{}\begin{matrix}u\left(1\right)=\dfrac{1}{2}\\u\left(n+1\right)=\dfrac{u\left(n\right)}{n+1}\end{matrix}\right.\)
a, CM : với mọi n thì 0<u(n) và \(\dfrac{u\left(n\right)}{n+1}\)\(\le\dfrac{1}{2}\)
b, Từ đó suy ra limu(n)=0
8 tháng 2 2021 lúc 22:43
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?