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May 3, 2023 · The sum of the first n natural number is given by the formula: \(\sum_1^n=\left[\frac{n\left(n+1\right)}{2}\right]\). where n is the natural number. The sum of first n natural numbers as read above can be defined with the help of arithmetic progression.
Jun 2, 2024 · Sum of the first n natural numbers formula is given by [n (n+1)]/2. In this article, we will learn about the sum of natural numbers, the sum of natural numbers definition, the sum of natural number formula, the derivation of the sum of natural number formula and solve some examples.
The sum of natural numbers formula is used to find the sum of the natural numbers up to n terms. i.e., 1 + 2 + 3 + 4 + 5 + .... up to n terms. To derive the formula, we need to use the sum of the arithmetic progression formula, because the natural numbers are arranged in an arithmetic sequence.
Sum of n terms of AP = n/2[2a + (n – 1)d] For AP of natural numbers, a = 1 and d = 1, Sum of n terms S n of this AP can be found using the formula-Sn = n/2[2×1+(n-1)1] S n = n(n+1)/2. Hence, this is the formula to calculate sum of ‘n’ natural numbers. Solved Examples on Sum of n Terms. Some examples will enhance the understanding of the ...
Apr 19, 2023 · Program to Find the Sum of First N Natural Numbers. A simple solution is to do the following. 1) Initialize : sum = 0 2) Run a loop from x = 1 to n and do following in loop. sum = sum + x.
The series \(\sum\limits_{k=1}^n k^a = 1^a + 2^a + 3^a + \cdots + n^a\) gives the sum of the \(a^\text{th}\) powers of the first \(n\) positive numbers, where \(a\) and \(n\) are positive integers. Each of these series can be calculated through a closed-form formula.
Sep 5, 2022 · The task is to find the sum of the sum of first n natural number. Examples: Input: n = 3. Output: 10. Explanation: Sum of first natural number: 1. Sum of first and second natural number: 1 + 2 = 3. Sum of first, second and third natural number = 1 + 2 + 3 = 6. Sum of sum of first three natural number = 1 + 3 + 6 = 10.
