1. 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 Calculus II

2. 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: 129437, 2, 13, 9859, 487, 12, 84, 7437, etc...  A series is the addition of a list of numbers: Eg: 2+4+6+8+10+12+14+16+18+20+22+24+etc... Eg: 129437+2+13+9859+487+12+84+7437+etc...

6. Note: (i)

7. (ii)

9. 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

11. Eg:

14. Ex: