The mathematical formula provided in the image represents the sum of squares of odd numbers up to $(2n-1)^2$. It is expressed as:

$1^2 + 3^2 + 5^2 + \dots + (2n-1)^2 = \frac{n(2n-1)(2n+1)}{3}$

Explanation:

1. Odd Numbers: Odd numbers can be written as $2k-1$, where $k = 1, 2, 3, \dots, n$.
2. Squaring Odd Numbers: The squares of these odd numbers are $(2k-1)^2$.
3. Sum: The sum is taken over the first $n$ odd numbers.

The formula derives from summing a sequence of squares of odd numbers, and its proof involves algebraic manipulation and summation properties.

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Relative Questions:

1. How is the formula for summing squares of odd numbers derived?
2. What is the difference between summing odd squares and even squares?
3. Can this formula be extended to higher powers of odd numbers?
4. How does this formula relate to summation of arithmetic series?
5. What are practical applications of summing odd squares?

Tip:

When summing sequences like squares or cubes, always check if there is a generalized formula to simplify the computation.