Microsoft Word sonlar ketma ketligi va uning limiti

nlim→∞xn = nlim→∞ = n n2 n3

I z o ҳ. Limitni hisoblashda kasrning surat va maхrajini n ning eng yuqori darajasi (n=3) ga bo’ldik.

5 ² − 3

5 – m i s o l. _n→∞ 2n2 + n + 2 n→∞
n2
Mustaqil bajarish uchun topshiriqlar.
I. Sonli ketma-ketlik limiti
lim a_n =^a ekanligi isbotlansin. (N( )ε ko‘rsatilsin) n→∞
1 . an = ;a= 2 2. an = ;a= 3

3. an ^=2n++21;a^=23 3n		4. an = 5n+−11;a= 5 n
n3 + 5. an = 3 +11;a= 12 2n		6. an = ;a= 2
7. an	= n−1 ;a= 1 2n+1 2				8. an ^=n++21n;a^=12 1

9. a_n ⁼ 23nn−₊1₁;a⁼ 3₂ 10. a_n ⁼ −
11. a_n = ;a⁼ 12. a_n = ;a=1

− 13. an ^=+6n1;a=−6 n		14. an = 7n+1;a= 12 14n
2n^2− 15. an ^=2 +31;a= 2 n		16. an ^=n+1;a^=1 3n 3

II. Sonli ketma-ketlik limiti hisoblansin.
2.
→∞ (4 n) (2 n)
3 . 4.
→∞ (2 n) (2 n) →∞ (2 n) (2 n)

^5. n→∞ (1+ 2n) + 4n2 6. →∞ (1 n₎

7 . 8.
→∞ (n 2) (n 1)

( n+1)³ +(n−1)³

9. lim 4 −1 10. →∞ (n 1) (n 1) n→∞ n
11. 12. (2−n)3

→∞ (n 2) (n 2) n→∞

1 3. 14.

→∞ (n 1) (n 1) →∞ (n 3) (n 2)