11A - Fisa de Lucru - Limite de Siruri
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Calcula‚ ti limitele ‚ sirurilor: Problema 1 1. x n = 1 n + (0; 3) n 2. x n = 1 n 2 + 1 2 n 3. x n = 1 n 5 2 3 2n+1 4. x n = 1 n! cos(n) 5. x n = 3 n 3 2 5 n 6. x n = 3 n! 7. x n = 1 n 2 + 3 5 n 2 8. x n = 3 n 2 1 2 n + 3 4 n 2 +1 9. x n = 2 n 3 n n+1 n 2 10. x n = 5 n 4 3 n+1 + 6 p n + 4 n 2 Problema 2 1. x n = n+2 2n+1 2. x n = 2n 2 +n+1 3n 2 n+5 3. x n = 3n 3 +n 2 +1 4n 3 2n 2 +5n1 4. x n = 6n 2 5n3 3n 3 +n 2 n+2 5. x n = 7n 2 +11n4 2n 2 +6n+1 6. x n = 3 n +2 n +sin n 3 n+1 +2 n+1 7. x n = 3n+(1) n n 2 5n8 8. x n = 3n 2 n+cos n 8n 2 +7n(1) n 9. x n = n+1 2n1 1 2 n 10. x n = n 2 2 n 11. x n = n 2 +n+1 3 n 12. x n = n 2 3 n 3n1 5n+7 13. x n = n 3 3n6 n 4 n 3 +n6 14. x n = 2n 2 n2 3n 3 +n 2 3 n 15. x n = 4n1 n 2 2n+3 n 2 n 16. x n = 2 n +n+2 3 n 5n+6 17. x n = 2 n +3 n +4 3 n +4 n 18. x n = n+3 2n6 5n 2 3n6 2n 2 1 4n 3 5n 2 5n 3 12n 2 n 19. x n = 2 n +n+2 2 n+1 +2n4 20. x n = 2 n +4 n +n 3 n +4 n2 +3n11 21. x n = n 2 2 n n+2 n1 22. x n = 1 2 n+1 2 n +n 2 5n1 23. x n = 1+2+3+:::+n n 2 24. x n = 1 2 +2 2 +:::+n 2 n 3 25. x n = 1 2 +3 2 +:::+(2n1) 2 n 3 26. x n = 12+23+:::+n(n+1) n 2 +2n+3 27. x n = 1 3 +2 3 +:::+n 3 n 4 28. x n = 13+35+:::+(2n1)(2n+1) n 3 +n+1 29. x n = 1 2 2+2 2 3+:::+n 2 (n+1) n 3 n 30. x n = 12 2 +23 3 +:::+n(n+1) 2 n 3 31. x n = 1+2+2 2 +2 3 +:::+2 n1 1+3+3 2 +3 3 +:::+3 n1 32. x n = 1+ 1 2 1 + 1 2 2 +:::+ 1 2 n1 1+ 1 3 1 + 1 3 2 +:::+ 1 3 n1 33. x n = 1+2+3+:::+n 1+2+2 2 +:::+2 n1 34. x n = n1 P k=0 ( 1 2 ) k n P k=1 (2k1)
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Transcript of 11A - Fisa de Lucru - Limite de Siruri
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Calculati limitele sirurilor:
Problema 1
1. xn = 1n + (0; 3)n
2. xn = 1n2 +12
n3. xn = 1n5
23
2n+14. xn = 1n! cos(n)
5. xn = 3n3 25
n6. xn = 3n!
7. xn = 1n2 + 35n2
8. xn = 3n212n +
34
n2+19. xn = 2
n
3n n+1n2
10. xn = 5n43n+1 +
6pn+ 4n2
Problema 2
1. xn = n+22n+1
2. xn = 2n2+n+1
3n2n+5
3. xn = 3n3+n2+1
4n32n2+5n1
4. xn = 6n25n3
3n3+n2n+2
5. xn = 7n2+11n4
2n2+6n+1
6. xn = 3n+2n+sinn3n+1+2n+1
7. xn =3n+(1)nn25n8
8. xn = 3n2n+cosn
8n2+7n(1)n
9. xn = n+12n1 12
n10. xn = n
2
2n
11. xn = n2+n+13n
12. xn = n2
3n 3n15n+7
13. xn = n33n6
n4n3+n6
14. xn = 2n2n23n3+n
23
n15. xn = 4n1n22n+3 n2n
16. xn = 2n+n+2
3n5n+6
17. xn = 2n+3n+43n+4n
18. xn = n+32n6 5n23n62n21 4n
35n25n312n2n
19. xn = 2n+n+2
2n+1+2n4
20. xn = 2n+4n+n
3n+4n2+3n11
21. xn = n22n
n+2n1
22. xn =12
n+1 2n+n25n123. xn = 1+2+3+:::+nn2
24. xn = 12+22+:::+n2
n3
25. xn =12+32+:::+(2n1)2
n3
26. xn =12+23+:::+n(n+1)
n2+2n+3
27. xn = 13+23+:::+n3
n4
28. xn =13+35+:::+(2n1)(2n+1)
n3+n+1
29. xn =122+223+:::+n2(n+1)
n3n
30. xn =122+233+:::+n(n+1)2
n3
31. xn = 1+2+22+23+:::+2n1
1+3+32+33+:::+3n1
32. xn =1+ 1
21+ 122+:::+ 1
2n11+ 1
31+ 132+:::+ 1
3n1
33. xn = 1+2+3+:::+n1+2+22+:::+2n1
34. xn =
n1Pk=0
( 12 )k
nPk=1
(2k1)
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Problema 3
1. xn =nPk=1
1k(k+1)
2. xn =nPk=1
1k(k+2)
3. xn =nPk=1
1k(k+3)
4. xn =nPk=1
1(2k1)(2k+1)
5. xn =nPk=1
1(3k2)(3k+1)
6. xn =nPk=2
k2
k21
7. xn =nPk=1
2k
3k
8. xn =
nPk=1
2k
nPk=1
3k
9. xn =
nPk=1( 12 )
k
nPk=1
k
10. xn =nPk=2
1k21
11. xn =
nPk=1
k
n+1 n2+1n
12. xn =
nPk=1
k(k+1)
n21 n+ 1
13. xn =
nPk=2
C2k
n2+1 n
14. xn =
nPk=1
kC1k
n2+1 n+ 1
15. xn =
nPk=0
Ckn
n22n+1
16. xn =
nPk=1
kCkn
n22n+1
17. xn =
nPk=2
C2k
nPk=3
C3k
18. xn =nPk=1
k2
n3+1
19. xn =nPk=1
k2
n3+k
20. xn =nPk=1
k(k+1)n3+k
21. xn =nPk=1
kn2+k
22. xn =nPk=1
2k+12n+k
23. xn =nPk=2
C2kn3+k
24. xn =nPk=2
C2k+C1k
n4+k
25. xn =nPk=1
( 12 )k
n2+k
26. xn =nPk=1
( 13 )k
3n+k
27. xn =nPk=1
2k
2n+k
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Problema 4
1. xn =12
nn+1
2. xn =13
n3n+1
3. xn =
n2n+1
2n1n+1
4. xn =2n2+n3n22
n2n3
5. xn =12
n2n+1
6. xn =13
n2+n+13n+1
7. xn =
n2n+1
2n21n+1
8. xn =4n2+n3n22
n2+n+12n3
9. xn =
5nn2+15n+1n2+2n+1
n2n+1
10. xn =32
n2+2n+1
11. xn =43
n2+13n+1
12. xn =3n22n+1
2n21n+1
13. xn =4n2+n3n22
n312n3
14. xn =5n2+(1)nn+1
4n2+1
2n53n21
15. xn =2n+n+13n+n2+1
3n1n+2
Problema 5
1. xn = n2+pn2+1
2n2+pn21
2. xn = n+pn2+n+1
2n+pn2n1
3. xn = n2+n+
pn2n
2n2n+pn4+n2+1
4. xn = 4n1pn2+n1
n2+pn24
5. xn = 3n2+pn4n
n2+p2n4+n3
6. xn = 3n5+p2n4n2
2n2p3n4+4n1
7. xn = 3n+3pn3+n12n1
8. xn = n+1p2n3n+1
3n2
9. xn =pn2+2n3+ 3pn33n2+1
2n+5
10. xn =pn(pn+1+
pn1)
n+1
11. xn =(pn+
pn1)(
pn1+pn+1)(pn+
pn+1)
npn
12. xn =pn(pn2+1+ 3
pn3+n+1)
n2n2
13. xn = npn2 n+ 1
14. xn = n+ 1pn2 + n+ 1
15. xn =pn2 + n+ 1 n+ 1
16. xn =pn2 + 1 n 2
17. xn =pn2 + n+ 1pn2 1
18. xn =pn2 + 3npn2 + 1
19. xn =pn+
pnpn
20. xn =qn+
pn+
pnpn
21. xn =qn+
pn+
pn
pn+
pn
22. xn =pn2 + n+ 1 +
pn2 1 + 1 2n
23. xn =pn+ 1 +
pn 1 2pn
24. xn = npnpn+ 1 +
pn 1 2pn
25. xn =3pn3 + n+ 1 n
26. xn =3pn3 + n2 + 1 n 1
27. xn =3pn3 + n2 + 1 + 3
pn3 + n+ 1 2n
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28. xn =3pn3 + n2 + 1 +
pn2 + n+ 1 2n
29. xn =3pn3 + n+ 1pn2 + n+ 1
30. xn =4pn4 + n2 + 1 n
31. xn =4pn4 + n2 + 1 4pn4 n2 + 1
Problema 6
