Special Series Sum Calculator

Add up natural numbers, squares, cubes, or odd numbers from the closed-form formula by entering the number of terms.

Input

Choose a series type and the number of terms n to compute the sum of natural numbers, squares, cubes, or odd numbers from a formula.

Series type

Number of terms n

Formula used: n(n+1)/2

Sum of natural numbers (n = 10)

Formula

n(n+1)/2

Terms n

Last term

Series preview

1 , 2 , 3 , 4 , 5 , 6 , …

Each type is computed with a well-known closed-form formula. The sum is always an integer.

The sum of natural numbers uses n(n+1)/2, the total of all integers from 1 up to n.
The sum of squares uses n(n+1)(2n+1)/6, the total of the squares from 1 squared to n squared.
The sum of cubes uses the square of n(n+1)/2, which equals the square of the sum of natural numbers.
The sum of odd numbers equals n squared. Adding the first n odd numbers 1, 3, 5, and so on always gives a perfect square.
Enter an integer of 1 or more for the number of terms n. The sum is always an integer for every series type.

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