Math Problem Statement

What is the sum of all natural numbers from 1 to 40

Solution

The sum of all natural numbers from 1 to 40 can be found using the formula for the sum of an arithmetic series:

Sn=n2×(a+l)S_n = \frac{n}{2} \times (a + l)

Where:

  • nn is the number of terms (in this case, 40),
  • aa is the first term (which is 1),
  • ll is the last term (which is 40).

Substitute the values:

S40=402×(1+40)=20×41=820S_{40} = \frac{40}{2} \times (1 + 40) = 20 \times 41 = 820

So, the sum of all natural numbers from 1 to 40 is 820.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What is the sum of all natural numbers from 1 to 100?
  2. How do you calculate the sum of even numbers from 1 to 40?
  3. What is the sum of odd numbers from 1 to 40?
  4. How can you derive the formula for the sum of an arithmetic series?
  5. What is the sum of the first 50 terms of the sequence 3, 6, 9, 12,...?

Tip: You can use the same arithmetic series formula to sum consecutive numbers or any regularly spaced sequence.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Series
Summation of Natural Numbers

Formulas

Sum of an arithmetic series: S_n = (n/2) × (a + l)

Theorems

Arithmetic Series Theorem

Suitable Grade Level

Grades 6-8