Show that the alternating harmonic series
1 - 1 / 2 + 1 / 3 - 1 / 4 + 1 / 5 - 1 / 6 + ...
(Whose sum is actually In 2 ( 0.69) can be rearranged to converge to 1.3 by using the following steps.
(a) Take enough of the positive terms
1 + 1 / 3 + 1 / 5 + ...
To just exceed 1.3.
(b) Now add enough of the negative terms
- 1 / 2 - 1 / 4- 1 / 6 - ...
So that the partial sum Sn falls just below 1.3.
(c) Add just enough more positive terms to again exceed 1.3, and so on?