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:

 




S

n


=

∑

k
=
1


n




1

k

2






{\displaystyle S_{n}=\sum _{k=1}^{n}{\frac {1}{k^{2}}}}




 and compute   




S

1000




{\displaystyle S_{1000}}




This approximates the   zeta function   for   S=2,   whose exact value

 



ζ
(
2
)
=



π

2


6




{\displaystyle \zeta (2)={\pi ^{2} \over 6}}


is the solution of the Basel problem.




' FB 1.05.0 Win64
 
Const pi As Double = 3.141592653589793
 
Function sumSeries (n As UInteger) As Double
  If n = 0 Then Return 0
  Dim sum As Double = 0
  For k As Integer = 1 To n
    sum += 1.0/(k * k)
  Next
  Return sum
End Function
 
Print "s(1000) = "; sumSeries(1000)
Print "zeta(2) = "; Pi * pi / 6
Print
Print "Press any key to quit"
Sleep