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Sum of series
OnSolver.com allows you to find the sum of a series online. Besides finding the sum of a number sequence online, server finds the partial sum of a series online. This is useful for analysis when the sum of a series online must be presented and found as a solution of limits of partial sums of series. Compared to other sites, www.OnSolver.com has a huge advantage, because you can find the sum of not only numerical but also functional series, which will determine the convergence domain of the original series, using the most known methods. According to the theory, a necessary condition for a numerical sequence convergence is that limit of common term of series is equal to zero, when the variable approaches infinity. However, this condition is not sufficient to determine the convergence of numerical series online. If the series does not converge, OnSolver.com will indicate this with a relevant message. For series convergence determination a variety of sufficient criterions of convergence or divergence of a series have been found. The most popular and commonly used of these are the criterions of D'Alembert, Cauchy, Raabe; numeric series comparison, as well as the integral criterion of convergence of numerical series. A special place among numeric series is occupied by such in which the signs of the summands are strictly alternated, and absolute values of the numeric series monotonously subside. It turns out for such numerical series that the necessary sign of convergence is also sufficient, that is the limit of the common term of series is equal to zero when the variable approaches infinity. There are many different sites on which there are servers presented to calculate the sum of a series, as well as to develop functions into a series at some point of the domain of this function. To develop a function into a series online is not difficult for those servers, but addition of functional series, each term of which, in contrast to numerical series, is not a number, but a function is virtually impossible due to lack of the necessary technical resources. For www.OnSolver.com there is no such problem.