Problem Statement

Compute the   nth   term of a series,   i.e. the sum of the   n   first terms of the corresponding sequence.
Informally this value, or its limit when   n   tends to infinity, is also called the sum of the series, thus the title of this task. For this task, use:

This approximates the   zeta function   for   S=2,   whose exact value is the solution of the Basel problem.

Let's start with the solution:

: sum ( fn start count -- fsum )
  0e
  bounds do
    i s>d d>f dup execute f+
  loop drop ;

:noname ( x -- 1/x^2 ) fdup f* 1/f ;   ( xt )
1 1000 sum f.       \ 1.64393456668156
pi pi f* 6e f/ f.   \ 1.64493406684823