Unconditional and unconditional Convergence Coursework

Unconditional and unconditional Convergence - Coursework ExampleUnconditional and unconditional ConvergenceTheorem any absolutely convergent serial is unconditionally convergent.Conditional ConvergenceA convergent series is give tongue to to be conditionally convergent if it is not unconditionally convergent. Thus such a series converges in the arrangement given, but either there is some rearrangement that diverges or else there is some rearrangement that has a various sum.Theorem Every nonabsolutely convergent series is conditionally convergent. In fact, every nonabsolutely convergent series has a diverging rearrangement and can also be rearranged to sum to any preassigned value.The unordered sum of a sequence of concrete numbers, written as,_iNai has an apparent connection with the ordered sum _(i=1)aiThe answer is twain have same convergence.Theorem A necessary and sufficient condition for _iNai to converge is that the series _(i=1)ai is absolutely convergent and in this cas e_(i=1)ai=_(i)ai