In the problem of convergence and divergence of higher mathematics series, why is it proved that the original series is not absolutely convergent and is said to be divergent? Can't be conditional income. It is proved here that the original series does not converge when the limit of the absolute value of the last term is +∞.

Because the limit of the absolute value of the latter term is greater than the limit of the former term by +∞, it can always be found that the absolute value of the latter term is getting bigger and bigger from a certain term. Then the series with increasing absolute value, even the staggered series, cannot converge.