What is the sum of odd numbers from 1 to 4000? Here we will show you step-by-step how to calculate the sum of odd numbers from 1 to 4000.
Step 1) We start by finding the first (F) and last (L) odd numbers from 1 to 4000. It is easy to do that by simply looking at the numbers. The first odd number is 1, and the last odd number is 3999.
F = 1
L = 3999
Step 2) Next, we calculate the total odd numbers (T) there are from 1 to 4000, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (3999 - 1 + 2) ÷ 2
T = 4000 ÷ 2
T = 2000
Step 3) Finally, we use the information from Step 1 and Step 2, and another formula, to calculate the sum of odd numbers from 1 to 4000, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (2000 ÷ 2) × (2 × 1 + (2 × (2000 - 1))
Sum = 1000 × (2 + 3998)
Sum = 1000 × 4000
Sum = 4000000
Sum of odd numbers from 1 to 4000 = 4000000
Sum of Odd Numbers Calculator
Please use the tool below to calculate the sum of odd numbers for another set of numbers.