if the nth term of a series as n approaches infinity does not approach zero, then the sum of the series diveres

the integral of a positive, continuous, decreasing function perfectly modeling a series will diverge if the sum of the series diverges and converges if the sum of the series conver

if a series 'a' is always less than a series 'b', and if 'b' converges, then 'a' converges. also, if 'a' diverges, then 'b' diverges

if the limit as n approaches infinity of the nth term of 'a' divided by the nth term of 'b' is equal to a finite and positive value, then they either both converge or both diverge

if the limit as n approaches infinity of the absolute value of the n+1th term of 'a' divided by the nth term of 'a' is equal to L, the series converges if L1, and is inconclusive i

if the limit as n approaches infinity of the nth root of the absolute value of the nth term of 'a' equals L, the series converges if L1, and is inconclusive if L=1

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