Does this pattern have a practical application?

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Nikita Ry2018-10-20 21:00:02

Mathematics

Nikita Ry, 2018-10-20 21:00:02

Does this pattern have a practical application?

It recently dawned on me (probably someone once realized it too) that if we calculate the sum of a convergent series using the formula: , where n is the order of the derivative (in addition to the ordinal number of the term), f (x) is some polynomial, then the root of the resulting polynomial is 1 less than the root of the original polynomial. For example, if , then the sum of the series . I have a question, where can this regularity be used?

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