# 10.4  Error Estimates
# Art Belmonte, Summer 1996
# These are the shaded gray examples which appear in Section 10.4.
> restart; a:=n->1/n^2; Sum(a(n), n=1..50);
> S50:=evalf("); error:=evalf(Pi^2/6 - S50);

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


                               50
                              -----
                               \     1
                                )   ----
                               /      2
                              -----  n
                              n = 1


                          S50 := 1.625132734


                         error := .019801334

> Int(1/x^2, x=51..infinity); l:=evalf(");
> Int(1/x^2, x=50..infinity); u:=evalf(");

                            infinity
                           /
                          |           1
                          |          ---- dx
                          |            2
                         /            x
                           51


                          l := .01960784314


                            infinity
                           /
                          |           1
                          |          ---- dx
                          |            2
                         /            x
                           50


                          u := .02000000000

> lower:=l+S50; upper:=u+S50;
> midpoint:=(lower + upper) / 2;
> maxerror:=(upper - lower) / 2;

                         lower := 1.644740577


                         upper := 1.645132734


                       midpoint := 1.644936656


                       maxerror := .0001960785

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