Giới hạn hữu hạn của dãy số

[ThanhTam]

Giới hạn của dãy số gồm:
1. Giới hạn hữu hạn: [Only registered and activated users can see links] 7B%7D+f%5Cleft%28+n+%5Cright%29+%3D+L+%5Cin+R&bg=ffffff&fg=333333&s=0
2. Giới hạn vô cực: [Only registered and activated users can see links] 7B%7D+f%5Cleft%28+n+%5Cright%29+%3D++%5Cpm+%5Cinft y&bg=ffffff&fg=333333&s=0
3. Giới hạn đưa về giới hạn hữu hạn hoặc vô cực.
khi làm bài chúng ta phải dự đoán được dạng bài đó thuộc dạng nào để từ đó áp dụng một số thủ thuật, nguyên tắc cho phù hợp.
I. giới hạn hữu hạn:
1. vài giới hạn đặc biệt:
[Only registered and activated users can see links] 5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C lim+%7D%5Climits_%7B%7D+%5Cfrac%7B1%7D%7Bn%7D+%3D+ 0%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C+ %5CRightarrow+%5Clim+%5Cfrac%7B1%7D%7B%7Bn%5Ek+%7D %7D+%3D+0%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2 C%5C%2C%5C%2C%5Cleft%28+%7Bk+%5Cin+N%5E%2A+%7D+%5C right%29&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5Clim+q%5En++%3D+0%5C %2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2Cneu%5C%2C%5 C%2C%5C%2C%5Cleft%7C+q+%5Cright%7C+%3C+1&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5Clim+c+%3D+c&bg=ffffff&fg=333333&s=0
2. Định lý về giới hạn hữu hạn:
[Only registered and activated users can see links] mits_%7B%7D+u_n++%3D+a%5C%2C%5C%2C%5C%2C%5C%2C%5C% 2C%3B%5C%2C%5C%2C%5C%2C%5C%2C%5Clim+v_n++%3D+b%5C% 2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C+%5CRightarrow&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] 5C%2C%5Clim+%7D%5Climits_%7B%7D+%5Cleft%28+%7Bu_n+ +%5Cpm+v_n+%7D+%5Cright%29+%3D+a+%5Cpm+b&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] Clim+%5Cleft%28+%7Bu_n+.v_n+%7D+%5Cright%29+%3D+a. b&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] Clim+%5Cleft%28+%7B%5Cfrac%7B%7Bu_n+%7D%7D%7B%7Bv_ n+%7D%7D%7D+%5Cright%29+%3D+%5Cfrac%7Ba%7D%7Bb%7D% 5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C %2C%5C%2C%5C%2C%5C%2C%5Cleft%28+%7Bb+%5Cne+0%7D+%5 Cright%29&bg=ffffff&fg=333333&s=0
[Only registered and activated users can see links] ge+0%2C%5Cforall+n%3B%5C%2C%5C%2C%5C%2C+%5CRightar row+a+%5Cge+0%5C%2C%5C%2C%5C%2C%5C%2Cva%5C%2C%5C%2 C%5C%2C%5C%2C%5Clim+%5Csqrt+%7Bu_n+%7D++%3D+%5Csqr t+a&bg=ffffff&fg=333333&s=0
3. Một số dạng bài tập điển hình tính giới hạn các dãy số:
a. [Only registered and activated users can see links] mits_%7B%7D+%5Cfrac%7B%7B2n%5E3++%2B+3n+-+1%7D%7D%7B%7B3+%2B+5n%5E2++-+4n%5E3+%7D%7D&bg=ffffff&fg=333333&s=0
b. [Only registered and activated users can see links] 7B%7D+%5Cfrac%7B%7B%5Csqrt+%7Bn%5E2++%2B+1%7D+%7D% 7D%7B%7B2n%7D%7D&bg=ffffff&fg=333333&s=0
c. [Only registered and activated users can see links] 7B%7D+%5Cfrac%7B%7B3%5En++%2B+5%5E%7Bn+%2B+1%7D+%7 D%7D%7B%7B1+-+5%5En+%7D%7D&bg=ffffff&fg=333333&s=0
d. [Only registered and activated users can see links] 7B%7D+%5Cleft%28+%7Bn+-+%5Csqrt+%7Bn%5E2++%2B+2n%7D+%7D+%5Cright%29&bg=ffffff&fg=333333&s=0

[ThanhTam]

[Only registered and activated users can see links] 7B%7D+f%5Cleft%28+n+%5Cright%29+%3D++%5Cpm+%5Cinft y&bg=ffffff&fg=333333&s=0
1. Một vài giới hạn đặc biệt:
a. [Only registered and activated users can see links] 7B%7D+n%5Ek++%3D++%2B+%5Cinfty+%5C%2C%5C%2C%5C%2C% 5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5Cleft%28+%7Bk +%5Cin+N%2A%7D+%5Cright%29&bg=ffffff&fg=333333&s=0
b. [Only registered and activated users can see links] 7B%7D+q%5En++%3D++%2B+%5Cinfty+%5C%2C%5C%2C%5C%2C% 5C%2C%5C%2Cneu%5C%2C%5C%2Cq+%3E+1&bg=ffffff&fg=333333&s=0
2. Các phép toán về giới hạn vô cực:
a. [Only registered and activated users can see links] 7Bl%7D%5Cmathop+%7B%5Clim+%7D%5Climits_%7B%7D+u_n+ +%3D+a+%5C%5C%5Cmathop+%7B%5Clim+v_n++%3D+%5Cpm+%5 Cinfty+%7D%5Climits_%7B%7D+%5C%5C%5Cend%7Barray%7D +%5Cright.+%5CRightarrow+%5Cmathop+%7B%5Clim+%7D%5 Climits_%7B%7D+%5Cfrac%7B%7Bu_n+%7D%7D%7B%7Bv_n+%7 D%7D+%3D+0&bg=ffffff&fg=333333&s=0
b. [Only registered and activated users can see links] 7Bl%7D%5Cmathop+%7B%5Clim+u_n++%3D+a+%3E+0%7D%5Cli mits_%7B%7D%5C%5C%5Cmathop+%7B%5Clim+v_n++%3D+0%7D %5Climits_%7B%7D++%5C%5Cv_n++%3E+0%2C%5Cforall+n+% 5C%5C%5Cend%7Barray%7D+%5Cright.+%5CRightarrow+%5C mathop+%7B%5Clim+%7D%5Climits_%7B%7D+%5Cfrac%7B%7B u_n+%7D%7D%7B%7Bv_n+%7D%7D+%3D++%2B+%5Cinfty&bg=ffffff&fg=333333&s=0
c. [Only registered and activated users can see links] 7Bl%7D%5Cmathop+%7B%5Clim+%7D%5Climits_%7B%7D+u_n+ +%3D++%2B+%5Cinfty++%5C%5C%5Cmathop+%7B%5Clim+v_n+ +%3D+a+%3E+0%7D%5Climits_%7B%7D%5C%5C+%5Cend%7Barr ay%7D+%5Cright.+%5CRightarrow+%5Cmathop+%7B%5Clim+ %7D%5Climits_%7B%7D+u_n+.v_n++%3D++%2B+%5Cinfty&bg=ffffff&fg=333333&s=0
3. Các dạng bài tập điển hình:
a. [Only registered and activated users can see links] 7B%7D+%5Cleft%28+%7Bn%5E3++-+3n%5E2++%2B+4%7D+%5Cright%29&bg=ffffff&fg=333333&s=0
b. [Only registered and activated users can see links] 7B%7D+%5Cfrac%7B%7Bn%5E3++%2B+3n+-+1%7D%7D%7B%7Bn%5E2++-+n+%2B+1%7D%7D&bg=ffffff&fg=333333&s=0
c. [Only registered and activated users can see links] 7B%7D+%5Cleft%28+%7B%5Csqrt+%7Bn%5E2++-+3n%7D++%2B+n%7D+%5Cright%29&bg=ffffff&fg=333333&s=0