### Compulsion of a linear equation system to the development of analytic formulas for the sumsof some finite series with the help of special computer programming

Pages 181-186

The article presents a convincing system of mathematical reasoning allowing us to pass over the stages of recurrent formulas as well as the induction methods in the pro- cess of developing analytic formulas using computer programs. The article elaborates the ideas on how to make the computer derive analytic formulas. The author offers us a generalization consisting in using the method of summing up to the more wide range of series, as well as finding approximate specific solutions to some differential equations and summarizations, which can occur, for example, in finite element method. The suggested method of summing the degrees with the coefficient is generalized to:a) The total formulas for the powers degrees of real numbers which are not the rational numbers. This will lead to approximate results.b) The representation of sums is connected to the solutions of certain differential equations (Cauchy problem), where we can obtain the partial equations in the form of power series with rational coefficients.

DOI: 10.22227/1997-0935.2014.1.181-186

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