#Ruby, 122 77 65 bytes

Thanks to Sherlock for shaving off 10 bytes.

require'prime'
->n{Prime.take(n).map{|x|1-2r/(x*x+1)}.reduce(:*)}

Defines an anonymous function that takes a number and returns a Rational.

Ruby, 122 77 65 bytes

Thanks to Sherlock for shaving off 10 bytes.

require'prime'
->n{Prime.take(n).map{|x|1-2r/(x*x+1)}.reduce(:*)}

Defines an anonymous function that takes a number and returns a Rational.

#Ruby, 122 77 67 bytes

Thanks to Sherlock for shaving off 10 bytes.

require'prime'
->n{p Prime.take(n).map{|x|1-2r/(x*x+1)}.reduce(:*)}

Defines an anonymous function that takes a number and outputs the result to STDOUT as (numerator/denominator).

#Ruby, 122 77 65 bytes

Thanks to Sherlock for shaving off 10 bytes.

require'prime'
->n{Prime.take(n).map{|x|1-2r/(x*x+1)}.reduce(:*)}

Defines an anonymous function that takes a number and returns a Rational.

#Ruby, 122 77 67 bytes

require'prime'
->n{p Prime.take(n).map{|x|1-2r/(x*x+1)}.reduce(:*)}

Defines an anonymous function that takes a number and outputs the result to STDOUT as (numerator/denominator).

#Ruby, 122 77 67 bytes

Thanks to Sherlock for shaving off 10 bytes.

require'prime'
->n{p Prime.take(n).map{|x|1-2r/(x*x+1)}.reduce(:*)}

Defines an anonymous function that takes a number and outputs the result to STDOUT as (numerator/denominator).