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Increasing Sequence

For a sequence {a_n}, if a_(n+1)-a_n>0 for n>=x, then a_n is increasing for n>=x. Conversely, if a_(n+1)-a_n<0 for n>=x, then a_n is decreasing for n>=x.

If a_n>0 and a_(n+1)/a_n>1 for all n>=x, then a_n is increasing for n>=x. Conversely, if a_n>0 and a_(n+1)/a_n<1 for all n>=x, then a_n is decreasing for n>=x.

See also

Decreasing Sequence, Sequence

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Cite this as:

Weisstein, Eric W. "Increasing Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IncreasingSequence.html

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