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#difference

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jwls

So, I learned something this past weekend about sequential exponential numbers, and how they can be verified through addition and subtraction no matter how high the exponents go.

Is this a known thing?

For example:

Every sequential ^2 has a once nested difference that increases by 2 and it's every odd number.

Every sequential ^3 has a twice nested difference of 6, which the first set of differences create a number which must then be subtracted from the next difference to see this pattern.

Every sequential ^4 has a thrice nested difference of 24, which the first set of differences create a number which must then be subtracted from the next set, followed by the third set to see this pattern.

Every sequential ^5 has a quaternary nested difference of 120, which means requires subtracting the sets four times to see the pattern.

So this validates ^6 at the fifth set of differences will provide a pattern of 720, ^7 at the sixth set will provide a pattern of 5040 and so on.

What is this called? Is there a simplified equation that shows this? Any and all help is much appreciated. Thanks!

#math#sums#difference
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