My cAlcULus nOTe...

[The divergence test]

(a) If limU≠０,then the series ΣU diverges.
(b) If limU＝０,then the series ΣU may either converge or diverge.

[The integral test]

Let ΣU be a series with positive terms. If f is a function that is decreasing and continuous on an interval [1,∞) and such that U＝f(k) for all k≧1, then ΣU and ∫f(x) dx both converge or both diverge.

[The comparison test]

Let Σa and Σb be series with nonnegative terms and suppose that ０≦a≦b
(a) If Σb converges, then Σa also converges.
(b) If Σa diverges, then Σb also disverges.