Find sum of all odd square numbers

Thread starter chwala
Start date Apr 8, 2024
Tags

Square Sum

In summary, the task involves calculating the sum of all odd square numbers. Odd square numbers are generated by squaring odd integers (1, 3, 5, 7, etc.). The sum can be expressed mathematically, and it can be derived using the formula for the sum of squares of odd numbers or computed by iterating through a defined range of odd integers, squaring each, and aggregating the results. The process yields a finite or infinite sum depending on the specified limits.

Apr 8, 2024

chwala

Gold Member

Homework Statement: see attached

Relevant Equations: sum of series.

There is a mistake on this textbook (The mistake is pretty obvious) but hey I hope I did not miss something...

ought to be ##40425 - 19600##

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Apr 9, 2024

Mark44

Mentor

Insights Author

chwala said:

ought to be 40425

Agreed.

FAQ: Find sum of all odd square numbers

What are odd square numbers?

Odd square numbers are the squares of odd integers. For example, the first few odd integers are 1, 3, 5, 7, and their squares are 1, 9, 25, 49, respectively. Thus, the odd square numbers are 1, 9, 25, 49, and so on.

How do you find the sum of all odd square numbers up to a certain limit?

To find the sum of all odd square numbers up to a certain limit, first identify all odd integers within that limit, square each of them, and then add those squared values together. For example, to find the sum of odd square numbers up to 25, you would consider the squares of 1, 3, 5, and so on, up to 5, which gives you 1 + 9 + 25 = 35.

Is there a formula to calculate the sum of odd square numbers?

Yes, there is a formula to calculate the sum of the first n odd square numbers. The sum can be expressed as n(2n - 1)(2n + 1)/3, where n is the number of odd integers you are considering. This formula allows you to quickly compute the sum without having to manually square and add each odd number.

What is the sum of the first five odd square numbers?

The first five odd square numbers are 1 (1^2), 9 (3^2), 25 (5^2), 49 (7^2), and 81 (9^2). Their sum is 1 + 9 + 25 + 49 + 81 = 165.

Can you provide a programming example to calculate the sum of odd square numbers?

Certainly! Here is a simple example in Python:

def sum_of_odd_squares(n):    return sum(i**2 for i in range(1, n+1, 2))result = sum_of_odd_squares(9)  # This will calculate the sum of odd squares up to 9print(result)  # Output will be 165