Divergence Test

Once again, do NOT misuse this test.  This test only says that a series is definite to diverge if the series terms do not go to zero in the limit.  If the series terms do occur to go to zero the series might or might not converge! Once again, remind the following two series,

Very first, we need to introduce the plan of a rearrangement. A rearrangement of a series is similarly what it might sound like; it is similar series with the terms rearranged into a different order.

For instance, consider the following the infinite series.

A rearrangement of this series is,

The issue we have the requirement to discuss here is that for some series each of these arrangements of terms can have different types of values in spite of the fact that they are using exactly similar terms.