Alternate series

In Mathematical, and more particularly in Analysis, a alternate series is a particular case of series to real coefficients , whose particular form makes it possible to have results of notable Convergence.

A series with real coefficients is known as alternate if its terms are alternated signs, i.e. if it is form:

$\backslash \; pm\; \backslash \; sum\_\; \{i=0\}\; ^\; \{+\; \backslash \; infty\}\; (-\; 1)\; ^ia\_i$

with a_i of the positive real numbers.

The main thing criterion of convergence concerning the alternate series makes it possible to show that certain alternated series not absolutely convergent are convergent, in particular the harmonic Série alternate; i.e. it succeeds where a more general criterion valid fails for all the numerical series. Such examples belong to the more general family of the semi-convergent series.

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