Super Summation 10: Palindromic Adding of Consecutive Integers

X2 = 1 + 2 + 3 +...+ (X - 1) + X + (X - 1) +...+ 3 + 2 + 1

(However, X must be a natural(or counting) number that's greater than or equal to 2)

Examples:

1 + 2 + 1 = 4, which is 2 squared!

1 + 2 + 3 + 2 + 1 = 9, which is 3 squared!

1 + 2 + 3 + 4 + 3 + 2 + 1 = 16, which is 4 squared!

1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = 25, which is 25 squared!

1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 36, which is 6 squared!

1 + 2 + 3 + 4 + 5 + 6 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 49, which is 7 squared!

Remember the formula for adding consecutive integers? Well, this trick is almost like a sequel to it! This time, you add all of the positive integers that are less than X twice! The total will always be equal to the square of X!

Negative numbers can be integers, too, but only positive ones are considered in this case!

What if the variable x is equal to 1? Then y will also be equal to 1, because you add nothing to it; adding nothing to anything makes no change!

Although Goldilocks mentioned the letter Y, it's not used as a variable in this math trick. However, she does mention the number 1, which is less than 2. Even if X = 1, then X2 will also be equal to 1 due to that number being idempotent. She also says that there would be nothing to add to that number because it's the smallest natural number!

Here's the formula of this math trick in summation form:

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© Derek Cumberbatch