【欧拉计划第 6 题】和的平方与平方的和差值 Sum square difference

Problem 6 Sum square difference

The sum of the squares of the first ten natural numbers is：

large 1^2 2^2 3^2 cdots 10^2=385

The square of the sum of the first ten natural numbers is：

large (1 2 3 cdots 10)^2=55^2=3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is：

large 3025 - 385 = 2640

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

问题 6 和的平方与平方的和差值

前十个自然数的平方的和为：

large 1^2 2^2 3^2 cdots 10^2=385

而前十个自然数和的平方为：

large (1 2 3 cdots 10)^2=55^2=3025

因此，前十个自然数的平方和与和的平方之间的差是：

large 3025 - 385 = 2640

求前一百个自然数的平方和与和的平方之间的差

思路分析

自然数的平方的和通项公式

large S(1)=frac{n(n 1)(2n 1)}{6}

自然数和的平方通项公式

large S(2)=left ( frac{n(n 1)}{2} right )^2

则和的平方与平方和差值通项公式为

large S(n)=S(2)-S(1)=left ( frac{n(n 1)}{2} right )^2-frac{n(n 1)(2n 1)}{6}

large =frac{n(n-1)(n 1)(3n 2)}{12}

代码实现

代码语言：javascript复制

/*
 * @Author: coder-jason
 * @Date: 2022-04-12 10:48:07
 * @LastEditTime: 2022-04-12 11:16:45
 */
#include <iostream>
using namespace std;

int main()
{
    int n = 100;
    long long int ans = n * (n - 1) * (n   1) * (3 * n   2) / 12;
    cout << ans;
    return 0;
}

答案：25164150

difference find numbers sum

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