Find the difference between the square of the sum and the sum of the squares of the first N natural numbers.
The square of the sum of the first ten natural numbers is (1 + 2 + ... + 10)² = 55² = 3025.
The sum of the squares of the first ten natural numbers is 1² + 2² + ... + 10² = 385.
Hence the difference between the square of the sum of the first ten natural numbers and the sum of the squares of the first ten natural numbers is 3025 - 385 = 2640.
Problem 6 at Project Euler http://projecteuler.net/problem=6
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
(ns difference-of-squares-test (:require [clojure.test :refer [deftest is]] [difference-of-squares :as dos])) (deftest square-of-sum-to-5 (is (= 225 (dos/square-of-sum 5)))) (deftest sum-of-squares-to-5 (is (= 55 (dos/sum-of-squares 5)))) (deftest difference-of-squares-to-5 (is (= 170 (dos/difference 5)))) (deftest square-of-sum-to-10 (is (= 3025 (dos/square-of-sum 10)))) (deftest sum-of-squares-to-10 (is (= 385 (dos/sum-of-squares 10)))) (deftest difference-of-squares-to-10 (is (= 2640 (dos/difference 10)))) (deftest square-of-sum-to-100 (is (= 25502500 (dos/square-of-sum 100)))) (deftest sum-of-squares-to-100 (is (= 338350 (dos/sum-of-squares 100)))) (deftest difference-of-squares-to-100 (is (= 25164150 (dos/difference 100))))
(ns difference-of-squares) (defn sum-of-squares [n] (quot (* n (inc n) (inc (* 2 n)) ) 6 ) ) (defn square-of-sum [n] (let [ sum (quot (* n (inc n)) 2) ] (* sum sum) ) ) (defn difference [n] (- (square-of-sum n) (sum-of-squares n) ) )
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