J's answer to Jia Yun's Junior College 1 H1 Maths Singapore question.

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J
J's answer
1024 answers (A Helpful Person)
A divergent series is one that does not converge. This means the series (which by definition is the sum of the terms in a sequence) does not have a limit and is not finite. Neither do the individual terms of the series converge/tend to any particular value.
In this case you have a oscillating/alternating series, where the value alternates between 0 and 1.
References for further reading :
mathworld.wolfram.com/DivergentSeries.html
mathworld.wolfram.com/ConvergentSeries.html
The study of this is beyond H2 level, let alone H1.