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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Week 1- Arithmetic sequence

6, 3,0, -3, -6

$t_n=t_1+(n-1)d$

$t_50=6+49(-3)$

$t_50=6+(-147)$

$t_50=-141$

$t_n=t_1+(n-1)d$

$t_n=6+(n-1)(-3)$

$t_n=6+(-3n)+3$

$t_n=(-3)=9$

$S_n=\frac{n}{2}(2t_1+(n-1)d)$

$S_{50}=\frac{50}{2}(2(6)+49(-3))$

$S_{50}=25(2(6)+49(-3))$

$S_{50}=25(12+-147)$

$S_{50}=25(-135)$

$S_{50}=-4725$