# 10.2  Series
# Art Belmonte, Summer 1996
# These are the shaded gray examples which appear in Section 10.2.
> restart; a:=n->1/n^2; Sum(a(n), n=5..9); value(");

                                       1
                            a := n -> ----
                                        2
                                       n


                                9
                              -----
                               \     1
                                )   ----
                               /      2
                              -----  n
                              n = 5


                               737641
                               -------
                               6350400

> Sum(a(n), n=1..infinity); value(");

                            infinity
                             -----
                              \       1
                               )     ----
                              /        2
                             -----    n
                             n = 1


                                     2
                               1/6 Pi

> a:=n->1/n; Sum(a(n), n=1..infinity); value(");

                            a := n -> 1/n


                             infinity
                              -----
                               \
                                )     1/n
                               /
                              -----
                              n = 1


                               infinity

> unassign('r'); a:=n->r^n; Sum(a(n), n=0..infinity); value(");

                                        n
                             a := n -> r


                             infinity
                              -----
                               \       n
                                )     r
                               /
                              -----
                              n = 0


                                   1
                               - -----
                                 r - 1

> a:=n->2^n; Sum(a(n), n=0..infinity); value(");

                                        n
                             a := n -> 2


                             infinity
                              -----
                               \       n
                                )     2
                               /
                              -----
                              n = 0


                               infinity

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