Math Problem Statement

Sum of first n natural numbers

Solution

The sum of the first nn natural numbers is given by the formula:

Sn=n(n+1)2S_n = \frac{n(n + 1)}{2}

Where:

  • SnS_n is the sum of the first nn natural numbers,
  • nn is the number of terms.

Example:

For n=5n = 5:

S5=5(5+1)2=5×62=15S_5 = \frac{5(5 + 1)}{2} = \frac{5 \times 6}{2} = 15

So, the sum of the first 5 natural numbers is 15.

Would you like a further explanation or to try an example with a different value of nn?

Related questions:

  1. What is the sum of the first 100 natural numbers?
  2. How does this formula come about?
  3. Can this formula be used for non-natural numbers (like fractions)?
  4. How does the formula change for odd or even numbers only?
  5. What is the sum of the first 50 even numbers?

Tip: Using this formula makes it easier to find the sum without having to add each term individually!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Arithmetic Series
Natural Numbers
Summation

Formulas

S_n = n(n + 1) / 2

Theorems

Sum of an arithmetic series

Suitable Grade Level

Grades 5-7