accumulator.clj

(defn accumulate1
  "accumulate a collection of terms from a to b using a combiner function"
  ([combiner init term a next b]
     (->> (iterate next a)
	  (take-while #(<= % b) ,)
	  (map term ,)
	  (reduce combiner init ,))))

(defn accumulate2
  "accumulate a collection of terms from a to b using a combiner function"
  ([combiner init term a next b]
     (reduce combiner init
	     (for [x (iterate next a)
		   :while (<= x b)]
	       (term x)))))

(defn accumulate3
  "accumulate a collection of terms from a to b using a combiner function"
  ([combiner init term a next b]
     (loop [a a, result init]
       (if (> a b)
	 result
	 (recur (next a) (combiner result (term a)))))))

(defn summation
  "sum f(n) from 0 to n-1"
  ([f n] (accumulate1 + 0 f 0 inc (dec n))))

(defn e**x [x n]
  (sumation #(/ (Math/pow x %) (factorial %)) n))