What is the recursion for computing the sum of the squares of the first n natural numbers? Denote it by Q(n).

The recursion for computing the sum of the squares of the first n natural numbers is:

Q(n) = Q(n-1) + n^2

with initial condition Q(0) = 0.

In other words, to compute Q(n), we can first compute Q(n-1) and then add n^2 to it. This process continues until we reach the base case Q(0), which is defined to be 0.

相关问题

7-2 Summation from 1 to n using recursion. 分数 10 全屏浏览题目 作者 Jinlan Xu 单位 杭州电子科技大学 Write a program in C to calculate the sum of numbers from 1 to n using recursion. Input: Input a positve integer n. Output : Compute the summation of 1+2+...+n. Sample of Input: 5 Sample of Output: 15

好的，我明白了你的问题。以下是一个使用递归计算从1到n的总和的C程序：

#include <stdio.h>

int sum(int n);

int main() {
    int n, result;
    printf("Input a positive integer n: ");
    scanf("%d", &n);
    result = sum(n);
    printf("Summation from 1 to %d is %d\n", n, result);
    return 0;
}

int sum(int n) {
    if (n == 0) {
        return 0;
    } else {
        return n + sum(n - 1);
    }
}

这个程序中，我们定义了一个名为“sum”的递归函数，它接受一个整数n作为参数，并返回从1到n的总和。在函数中，我们首先检查n是否为0，如果是，我们返回0作为基本情况。否则，我们通过递归调用sum函数来计算n-1的总和，并将结果与n相加，以获得n的总和。最后，在主函数中，我们获取用户输入的整数n，并将其作为参数传递给sum函数，以计算从1到n的总和，并将结果打印到控制台上。

希望这个程序能够帮助您解决问题！

Write a program in C to calculate the sum of numbers from 1 to n using recursion. Input: Input a positve integer n. Output : Compute the summation of 1+2+...+n. Sample of Input: 5 Sample of Output: 15

Sure, I can help you with that. Here's the C program to calculate the sum of numbers from 1 to n using recursion:

#include <stdio.h>

int sum(int n);

int main() {
    int n, result;
    printf("Enter a positive integer: ");
    scanf("%d", &n);
    result = sum(n);
    printf("The sum of numbers from 1 to %d is %d.\n", n, result);
    return 0;
}

int sum(int n) {
    if (n == 0) {
        return 0;
    } else {
        return n + sum(n-1);
    }
}

Explanation:

The program takes a positive integer `n` as input from the user and calls the `sum()` function with `n` as argument.

The `sum()` function is a recursive function that takes an integer `n` as input and returns the sum of numbers from 1 to `n`.

If `n` is 0, the function returns 0. Otherwise, it adds `n` to the sum of numbers from 1 to `n-1` by calling itself recursively with `n-1` as argument.

Finally, the program outputs the result, which is the sum of numbers from 1 to `n`.