|\^/|     Maple 9.5 (IBM INTEL LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2004
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> restart;
> f:=n->(1+1/n)^n;
                                                n
                             f := n -> (1 + 1/n)

> f(1);
                                       2

> f(2);
                                      9/4

> evalf(f(3));
                                  2.370370370

> for k from 1 to 10
> do
>     print("k=",k,"f(k)=",f(k),evalf(f(k)));
> od;
                            "k=", 1, "f(k)=", 2, 2.

                      "k=", 2, "f(k)=", 9/4, 2.250000000

                                         64
                       "k=", 3, "f(k)=", --, 2.370370370
                                         27

                                        625
                      "k=", 4, "f(k)=", ---, 2.441406250
                                        256

                                        7776
                      "k=", 5, "f(k)=", ----, 2.488320000
                                        3125

                                       117649
                     "k=", 6, "f(k)=", ------, 2.521626372
                                       46656

                                      2097152
                    "k=", 7, "f(k)=", -------, 2.546499697
                                      823543

                                      43046721
                    "k=", 8, "f(k)=", --------, 2.565784514
                                      16777216

                                     1000000000
                   "k=", 9, "f(k)=", ----------, 2.581174792
                                     387420489

                                     25937424601
                  "k=", 10, "f(k)=", -----------, 2.593742460
                                     10000000000

> g:=n->(1+1/n)^(n+1);
                                             (n + 1)
                          g := n -> (1 + 1/n)

> for k from 1 to 10
> do
>     print("k=",k,"g(k)=",g(k),evalf(g(k)));
> od;
                            "k=", 1, "g(k)=", 4, 4.

                      "k=", 2, "g(k)=", 27/8, 3.375000000

                                        256
                      "k=", 3, "g(k)=", ---, 3.160493827
                                        81

                                        3125
                      "k=", 4, "g(k)=", ----, 3.051757812
                                        1024

                                       46656
                     "k=", 5, "g(k)=", -----, 2.985984000
                                       15625

                                       823543
                     "k=", 6, "g(k)=", ------, 2.941897434
                                       279936

                                      16777216
                    "k=", 7, "g(k)=", --------, 2.910285368
                                      5764801

                                     387420489
                   "k=", 8, "g(k)=", ---------, 2.886507578
                                     134217728

                                    10000000000
                  "k=", 9, "g(k)=", -----------, 2.867971991
                                    3486784401

                                    285311670611
                 "k=", 10, "g(k)=", ------------, 2.853116706
                                    100000000000

> quit;
bytes used=357108, alloc=262096, time=0.01