One thing that I learned this week in pre Cal 11 is diverging and converging. Divering series means: there is no sum and it’s a finite or infinite geometric series; the formula used is . To find out if it is diverging you use r>1 or r<-1. Converging series means: there is a sum and it’s infinite or finite geometric series; the formula used is . To find out if it is converging you use -1<r<1 or -1<decimals <1.
Example of Diverging series :
Blue line : X |Y Orange line : X | Y
1 | 4 1 |4
2 | 8 2 | 1.6
3 | 16 3 |0.64
4 | 32 4 | 0.256
5 | 64 5 | 0.1024
6 | 128 6 | 0.04096
Example of Converging series:
purple line : X | Y Red line : X | Y
1 | 4 1 |4
2 |-8 2 | -1.6
3 |16 3 |0.64
4 |-32 4 | -0.256
5 | 64 5 | 0.1024
6 |-128 6 | -0.04096
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