If successive-term absolute value is less than previous-term absolute value, series converges {absolutely convergent} {convergence, series}.
Series can be convergent even if successive-term absolute value is not less than previous-term absolute value {conditionally convergent}. Conditionally convergent series can rearrange to make sum be any number.
constant times sequence
If sequence converges, limit of constant times sequence is constant times sequence limit.
uniform
Absolute value of partial sum S(n) minus sum from x = 1 to x = n of S(n) * x can be less than small value, for all x {uniform convergence}.
Mathematical Sciences>Calculus>Series>Convergence
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Date Modified: 2022.0224