homework binoms

(defun factorial (n)
  (let ((result 1))
    (dotimes (i n result)
      (setf result (* result (1+ i))))))

(defun combinations (m n)
  (/ (factorial m) (* (factorial n) (factorial (- m n)))))

(defun harmonic (n)
  (let ((result 0))
    (dotimes (i n result)
      (incf result
        (* (expt -1 i) (/ 1 (1+ i))
           (combinations n (1+ i)))))))

(defun question-1 (m)
  (let ((result 0))
    (dotimes (n (1+ m) result)
      (incf result
        (* (/ 1 (+ n 1)) (combinations m n))))))

(defun question-1-2 (m)
  (let ((result 0))
    (dotimes (n (1+ m) result)
      (incf result
        (/ (factorial m)
           (* (factorial (1+ n)) (factorial (- m n))))))))