Absolute value, Radicals, and roots

This week in Pre- Cal 11 I learned about Absolute Value and Radicals.

Absolute Value of a real number is defined as the principle square root of the square of a number, Principle Square Root is always a positive number, Square of a number is \sqrt{25} = 5 but is you have \sqrt[2]{25}=5 it is always a positive number in absolute value so it would be for both \mid 5\mid . Absolute value is always the distance from zero.

When using Roots & Radicals: the \sqrt [root]{radicand} the number in front of the root is the coefficient. if you have a square root it is always a positive in the radicand and the index is always a 2. If you have a cute root it is either negative or positive in the radicand and the index is always 3. The higher roots can be \sqrt [4]{positive}  \sqrt [5]{positive/negative}  \sqrt [6]{positive}

 

 

Week 2 – geometric series

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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