This week we learned the calculations that involve radicals such as add, subtract. In the case of add and subtract we need to convert the subjects that we are adding into mixed radicals with the same radican. EX: $\sqrt{12}+\sqrt{27},2\sqrt{3}+3\sqrt{3},5\sqrt{3}$ when the radicals have the same radican you will have to add the exponent of the mixed radical and keep the radican the same. For multiplication and division you can just apply the rules of multiplication and division on entire radicals with one exception, that is you can’t write denominator as a radical.

Week 3- Absolute Value

In this week’s classes, we learned the concept of absolute value…

Absolute value expresses the distance between numbers on a number line, due to the fact that there can’t be a negative distance as it is a scalar value, everything coming out of the “||” are positive. and the expression within absolute value get prioritization in an equation, such as

3×2+|2-3|, 6+1=7.

Sum of Infinite Geometric Series

In this week’s Math 11 Pre-Cal I learned that you can actually determine the exact Sum of Infinite Geometric Series in certain situations, when they are converges.( when -1<r<1) as with a rate less than 1 and greater than -1 the next term will get closer and closer to zero, therefore there is a determinable  sum. In the case of a diverging series, the  sum will get infinity big and therefor we can’t determine the exact sum.

The equation for the sum of an regular Geometric Series is

Sn=$\frac{a(1-r^n)}{1-r}$

When -1<r<1 $r^n$ approaches 0 as n increases indefinitely.

So, Sn approaches Sn= $\frac{a(1-0)}{1-r}$, therefor $S\infty= \frac{a}{1-r}$

EX:

A Infinite Geometric Series where r=0.5

8,4,2,1

$S\infty= \frac{8}{1-0.5}$ $S\infty= \frac{8}{0.5}$ $S\infty= {16}$

Week 1 – My Arithmetic Sequence

My Arithmetic Sequence:

21,23,25,27,29

The Sequence has a common difference of +2

Part one:

Tn=T1+(n-1)D

T50=21+(50-1)2

T50=21+49×2

T50=21+98

T50=119

Part two:

Sn=(T1+Tn) $\frac{n}{2}$

S50=(21+119) $\frac{50}{2}$

S50=140$\frac{50}{2}$

S50=140×25

S50=3500