1Series 1.1Alternating Series 1.2Absolute Convergence 1.3 Rearrangement of Series. 1.4Comparison Tests 1.5Ratio and Root Tests 1.6Other tests MAT 127 2.0.

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Presentation transcript:

1Series 1.1Alternating Series 1.2Absolute Convergence 1.3 Rearrangement of Series. 1.4Comparison Tests 1.5Ratio and Root Tests 1.6Other tests MAT Calculus II

Introduction Just to refresh your memory  A sequence is just a list of numbers: Eg: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, etc... Eg: , 2, 13, 9859, 487, 12, 84, 7437, etc...  A series is the addition of a list of numbers: Eg: etc... Eg: etc...

Note: (i)

(ii)

The BIG QUESTION is:  If you added up an INFINITE list of numbers, Would you eventually get a REGULAR NUMBER (not infinity) or would you get INFINITY?  If you get a Regular Number, your Series CONVERGES  If you get Infinity, this means your series DIVERGES

Eg:

Ex:

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