The <series> $\sum u_n$ has <absolute convergence> if $\sum|u_n|$ is a <convergent series>, meaning its nonnegative <partial sums> have a finite <limit>. <Absolute convergence> implies convergence of the original real or complex <series>. The converse fails: the <alternating harmonic series> converges, while its absolute-value <series> is the divergent <harmonic series>.

Solution

Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2001 / Paper 2 / 12 / b / ii / Solution

 Solution (source code)