80
Rozdział 4- Ciągi i szeregi
4.12. an = 4n — \/l6n2 + 6n — 5. 14.13. an = V4n2 + 5ra - 7 - 2n."
v 4.14. an = \/n2 — 1 — n.rQ
__ /V
i 4.15. an — y/n2 — n + 1 — n.— " V?
„ 4.16. an — \Ai4 + n2 — y/nĄ — n2.
4.38. an
4.39. an
4.40. an
4.41. an
= arcsin (\/n + 1 - y/n).
Vn2 - 1).
4.17. an
4.18. an
4.19. an
4.20. an
4.21. an
= V 3 n2 + 2n — 5 — n\/3. = Vn2 — 2n — \Zn2 + 2 n. = \/ 4n2 + n — 2\Jn2 — 1. = y/n + ^/n - \Jn- sfn.
__ _n_
\Ai2+l+\/27i2 + l "
4.22. an
4.23. (in
4.42. a„ = (tl)2".
4.43. o, = (1 - 2)2"
4.44. «„=(!_ X)4"
4.45. an = (2±S)2’*.
4.46. a„ = (1 + i)2"
4.47. a„ = (1 -
4.59. a,
4.60. ar
4.61. ar
4.62. an
4.63. an
4.64. an
4.65. an
4.66. an
4.24. an = '4.25. an =
4.26. an =
4.27. an =
4.28. an -
4.29. an =
4.30. an =
4.31. an =
4.32. an =
4.33. an =
4.34. an =
4.35. —
4.36. an —
4.37. an =
n—3
\/n2+n—\/n2+2
• A
\/9n24-3n+l —3n"
3n2 — -\/n3 +1 — n2 —2n+4 '
^n3 + n — n.
ś^n3 + 2n2 — n.
V^n3 + 2n — 1 — n.
\/n3 + 5 — n.
n(\/n3 + n — n).
4.48. a„ = (^)”2.
4.50. an =
4-52- =
4.53. a„ = (n±l)2”.
\/n3 — n — (n — 2).
^71^ + 277 — 71 n
\Zn3 —71+1—n 71 — 1
_71+1_
\Z9n3—3n+l—3n
5n_
\/8n3+n—n
1
\/8n3+5n—2n
4.54.
4.55.
4.56.
4.57.
4.58.
^71 — |
^n+2jn+! | |
a 71 = |
0 “ ^ |
r |
a 71 = |
(*+ |
2 71 |
a 71 : |
f n3 ) |
7i2—5n |
<2/1 ~ | |
(n2+2\ i 712—2 ) |
n 2 |
4.67. an
4.68. an
4.69. an
4.70. an
4.71. an
4.72. an
4.73. an
4.74. an
4.75. an
4.76. an
4.77. an
4.78. an
4.79. an