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Write program to approximate pi with Leibniz formula in Scheme?

I'm trying to figure out how to write a program to approximate pi with the Leibniz formula. The function takes an error, E, and somehow gives the pi approximation.

I'm not sure at all how to do this. I started writing a helper function but didn't know what to put in it. Any help?

Thanks!

Solution

  • The Leibniz formula for PI is a summation. The function will increment n until the summand for n is less than E.

    (define (leibniz err)
  (define (summand n)
    (/ (expt -1 n) (+ (* 2.0 n) 1)))
  (let summing ((result 0) (n 0))
    (let ((increment (summand n)))
      (if (< (abs increment) err)
          (* 4 (+ result increment))
          (summing (+ result increment) (+ n 1))))))