In Mathematics, a divergent sequence is an infinite sequence that is not convergent, meaning that we never find a greatest number in a sequence from which the whole sequence terms are smaller.
1. A sequence {aₙ} is said to diverge to ∞ if given k>0, however large, there exist a positive integer m (depending upon k) such that
we write it as
As shown in the figure we have taken aₙ on y-axis and its subscript on x-axis. Let suppose that k is a very large number. If the sequence need to diverge, then we will always find a term in a sequence which is greater then k. Therefore the sequence diverge to +∞.
2. A sequence {aₙ} is said to diverge to -∞ if given k>0, however large, there exist a positive integer m (depending upon k) such that
we write it as
Divergent sequence
1. A sequence {aₙ} is said to diverge to ∞ if given k>0, however large, there exist a positive integer m (depending upon k) such that
we write it as
2. A sequence {aₙ} is said to diverge to -∞ if given k>0, however large, there exist a positive integer m (depending upon k) such that
we write it as
Divergent series
The series ∑aₙ is said to diverge to ∞ if the sequence {sₙ} diverge to ∞. We write
The series ∑aₙ is said to diverge to -∞ if the sequence {sₙ} diverge to -∞. We write
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