Pre-Calculus, Week 2

One thing that I learned this week in pre Cal 11 is diverging and convergingDivering series means: there is no sum and it’s a finite or infinite geometric series; the formula used is S_n=\frac {a(r^{n}-1)}{r-1} . 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 S_\infty=\frac{a}{1-r} . 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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