The Weierstrass M-test can be used to test for this property.
For finite difference methods applied to PDEs, this property is equivalent to stability according to the Lax equivalence theorem. The Weierstrass M-test can be used to test for this property. A sequence of real numbers has this property if and only if it is a Cauchy sequence. For a series with both positive and negative terms, the (*) "absolute" form of this property is stronger than the usual form, only requiring that the terms go to zero. This property is possessed everywhere by the Taylor series for the exponential function, while other power series may have some finite "radius of" this property. Common tests to determine this property include the ratio test and the root test. For 10 points, give this mathematical term for approaching a limit.
For finite difference methods applied to PDEs, this property is equivalent to stability according to the Lax equivalence theorem.
convergence [or other word forms of "converge"]