There exist numerous classes of divergent series that converge in some generalized sense, since to each such divergent series some “generalized sum” may be assigned that possesses the most important properties of the sum of a convergent series. The Great Soviet Encyclopedia, 3rd Edition (1970-...
Homework Statement (a) Show that \sum \frac 1n is not convergent by showing that the partial sums are not a Cauchy sequence (b) Show that \sum \frac 1{n^2}...
He believed that all series should have a value, not necessarily a limit as for convergent series, and that the value should remain invariant irrespective of the method of evaluation. Via the key concept of regularisation, which results in the removal of the infinity in the remainder of a ...
In all of these works, the objective or cost function was assumed to be a convergent improper integral. That this may not be the case was realized by Ramsey in his seminal paper. To circumvent this he introduced what we now call the "optimal steady-state problem," which in Rarnsey's ...
The Integral Test compares the series to the integral of a related function and determines if the integral is convergent or divergent. If the integral is divergent, then the series is also divergent. What is the Comparison Test used for?