Математический анализ: Типовые расчеты по курсу. Исаев Г.П. - 41 стр.

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13.
()
1nn
1
u
n
+
=
.
14.
()( )
2n1nn
1
u
n
++
=
.
15.
2
2
n
n
1n
lnu
+
=
. 16.
n
n
n
n
!ne
u =
.
17.
n
n
n
n
!n3
u = .
18.
n2n
1
u
2
n
+
= .
19.
()
.
!n2
!1n
u
n
n
+
=
20.
()
!1n
n
u
n
+
= .
21.
4
5
n
n
nln
u = .
22.
2
3
2
n
n1
n1
u
+
+
= .
23.
()
!1n2
1
u
n
+
= .
24.
()
2
n
n
!n
n
u =
.
25.
()
n
n
3
!n2
u = .
26.
()
!n2
n
u
n
n
=
.
27.
()
!1n
3
u
n
n
+
= .
28.
n
n
n
!n
u = .
29.
()
n
n
n
!1n
u
+
= .
30.
()
.
!1n
n
u
3
4
n
+
=
41
                        1                                             1
13. u n =                               .   14. u n =                            .
                n (n + 1)                                    n (n + 1)(n + 2 )

                 n2 + 1                                 en n!
15. u n = ln                        .       16. u n =             .
                        n2                               nn

            3n n !                                                1
17. u n =           n
                            .               18. u n =                       .
                n                                            n2 + 2 n

            (n + 1)!                                       n
19. u n =                       .           20. u n =            .
                 n
                2 n!                                    (n + 1)!
                                                                       2
            ln n                                       ⎛1 + n2        ⎞
21. u n =               .                   22. u n = ⎜⎜      3
                                                                      ⎟ .
                                                                      ⎟
            4
                n5                                     ⎝1 + n         ⎠

                1                                        nn
23. u n =              .                    24. u n =             .
            (2 n + 1)!                                  (n !)2

            (2 n )!                                      nn
25. u n =                   .               26. u n =           .
                3n                                      (2 n )!

              3n                                        n!
27. u n =            .                      28. u n =         .
            (n + 1)!                                    nn

            (n + 1)!                                     3
                                                           n4
29. u n =                       .           30. u n =            .
                nn                                      (n + 1)!




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