Common questions

# What is the sum of the cubes of first n natural number?

## What is the sum of the cubes of first n natural number?

We know that sum of cubes of first n natural numbers is = (n(n+1)/2)2.

How do you find the sum of cubes of n natural numbers?

Solution:

1. We know the sum of the cubes of first n natural numbers (S) = {n(n+1)2}2.
2. Therefore, the sum of the cubes of first 12 natural numbers = {12(12+1)2}2.
3. We know the sum of the cubes of first n natural numbers (S) = {n(n+1)2}2.
4. Therefore, the sum of the cubes of first 25 natural numbers = {25(25+1)2}2.

### How do you find the sum of squares of n natural numbers in C?

The sum of squares of the first n natural numbers is found by adding up all the squares. Using Loops − the code loops through the digits until n and find their square, then add this to a sum variable that outputs the sum.

What is the formula for sum of cubes?

FAQ’s on Sum of Cubes Formula a3 + b3 formula is known as the sum of cubes formula it is read as a cube plus b cube. Its expansion is expressed as a3 + b3 = (a + b) (a2 – ab + b2).

## What is the sum of n natural numbers?

The formula of the sum of first n natural numbers is S=n(n+1)2 . If the sum of first n natural number is 325 then find n.

What is the sum of square of n natural numbers?

Sum of Squares of Natural Numbers

Sum of squares of n natural numbers n×(n+1)×(2n+1)6 n × ( n + 1 ) × ( 2 n + 1 ) 6
Sum of squares of first n even numbers 2n×(n+1)×(2n+1)3 2 n × ( n + 1 ) × ( 2 n + 1 ) 3
Sum of squares of first n odd numbers n×(2n+1)×(2n−1)3 n × ( 2 n + 1 ) × ( 2 n − 1 ) 3

### How do you find the sum of squares of n numbers?

Sum of Squares

1. Sum of squares refers to the sum of the squares of numbers.
2. Σ(xi + x̄)2
3. Proof: From the algebraic identities, we know;
4. Proof: From the algebraic identities, we know;
5. Proof:
6. Σ(2n)2 =[2n(n+1)(2n+1)]/3.
7. Proof:
8. Σ(2n-1)2 = [n(2n+1)(2n-1)]/3 is the required expression.

What is the formula for sum of odd numbers?

Sum of first two odd numbers is equal to 1 + 3 = 4 (4 = 2 x 2). Sum of first three odd numbers is equal to1 + 3 + 5 = 9 (9 = 3 x 3). Sum of first four odd numbers is equal to 1 + 3 + 5 + 7 = 16 (16 = 4 x 4).

## What is the sum of n?

The sum of n terms of AP is the sum(addition) of first n terms of the arithmetic sequence. It is equal to n divided by 2 times the sum of twice the first term – ‘a’ and the product of the difference between second and first term-‘d’ also known as common difference, and (n-1), where n is numbers of terms to be added.

What is the sum of first 100 natural number?

5050
Therefore, the sum of first 100 natural numbers = 5050.

### What is the sum of square of n terms?

Sum of Squares Formulas

In Statistics Sum of Squares: = Σ(xi + x̄)2
In Algebra Sum of Squares of Two Values: = a2 + b2 = (a + b)2 − 2ab
For “n” Terms Sum of Squares Formula for “n” numbers = 12 + 22 + 32 ……. n2 = n(n+1)(2n+1)/6

How to find sum of cubes of first n natural numbers?

Write a C program to find the sum of cubes of first n natural numbers. What is cube sum program written in c ? In this cube sum program , we find cube of individual digit of a number and find their sum .for example: 123 = 1^3 + 2 ^3 + 3^3.

## How to calculate the sum of n, n², or N³?

It turns out that the terms can be expressed quite concisely in terms of the Bernoulli numbers, as follows: ∑ k = 1 n k a = 1 a + 1 ∑ j = 0 a ( − 1) j ( a + 1 j) B j n a + 1 − j. na+1−j. ( − 1) a + 1 − i a + 1 ( a + 1 i) B a + 1 − i. . ∑ k = 1 n k a = 1 a + 1 n a + 1 + 1 2 n a + ( lower terms). na +(lower terms). 1 2 n a. na.

How to find sum of numbers in C program?

Area of a leaf inside a square in C Program? The concept of finding the sum of sum of integers is found such that first, we will find the sum of numbers up to n and then add all the sums to get a value which will be the sum of sum which is our desired sum. For this problem, we are given a number n up to which we have to find the sum of the sum.

### Which is the sum of all natural numbers up to 10?

The positive numbers 1, 2, 3… are known as natural numbers. The sum of natural numbers up to 10 is: The sum of natural numbers up to 10 is: sum = 1 + 2 + 3 + + 10