The square cumulative sum formula is a common sum formula in mathematics, which is used to calculate the sum of squares of a series of numbers. This formula can be expressed as: n(n+ 1)(2n+ 1)/6, where n is the number of numbers requiring sum.

Let's explain the meaning of this formula in detail.

First, we consider a series in which each number is 1, that is, {1, 1, 1, ..., 1}. This series has n 1.

Then, we can square this series and get {1, 1 2, 1 2, ..., 1 2}. This series has n12.

Next, we sum this series and get12+12+12+...+12 = n *12 = n.

If we substitute this result into the original formula, we will get:

n(n+ 1)(2n+ 1)/6=n(n+ 1)(2n+ 1)/6=n(n^2+n+n+ 1)/6=n^3+2n^2+n/6

This result is our square cumulative sum formula.

This formula has many applications in mathematics, such as solving problems such as graphic area and object volume. For example, you can use this formula to solve the area of a square or the volume of a cube.

In addition, this formula can also be extended to solve the sum of three numbers, the sum of four numbers, and so on, just by adding the corresponding terms to the original formula.

In addition to these applications, the square cumulative sum formula also has a very important application, that is, when solving the combination number. In the combination number, there is a very common formula called Pascal triangle, which is generated by square accumulation and summation formula. The value of any line or any number in Pascal's triangle can be quickly calculated by using the square accumulation summation formula.