Get down with the lingo
SeriesSeries is a sum of the terms of a sequence denoted by .
Alternating SeriesAn alternating series is one whose terms alternate between a positive and a negative sign.
Partial SumThe sum of n terms of a series is called the nth partial sum denoted by Sn.
Convergent SeriesWhen the sequence of partial sums Sn converges the series is convergent.
Convergent SequenceIf the limit of a sequence exists, the sequence is convergent.
Arithmetic SeriesThis occurs when the terms of a series form an arithmetic sequence.
Geometric SeriesThis occurs when the terms of a series form a geometric sequence.
Divergence TestWhen the nth term of a series does not approach 0, the series is divergent.
Alternating Series TestFor an alternating series , if the series is decreasing and passes the divergent test, the alternating series converges.
Ratio TestFor the series , if the limit is less than 1, the series converges. If L > 1, the series diverges and for L = 1, the test is inconclusive.
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