Deret Geometri : Scored Geometry and Geometric Series Addition Results

Geometric series can be written as follows :

a + ar² + ....... + arn-1

a : tribe initial
r : ratio
n : a lot of tribes

For the number of runs formula n geometry like this:

Sn = a(rn-1)/r-1 , jika r>1
= a(1-rn)/1-r , jika r<1 --> Exponential function (in n)

Description:

1. The ratio between two successive rate is fixed
2. Rows of geometry will rise, if for each n apply Un> Un-1
3. Rows of geometry will go down, if for n every valid Un4. Alternately up and down, if r <0
5. Valid relationships Un = Sn - Sn-1
6. If an odd number of tribes, the tribal center
7. Ut = sqrt(U1xUn) = sqrt(U2 X Un-1) dst.
8. If three numbers form a geometric sequence, then to facilitate the calculation, suppose that the numbers it is a / r, a, ar

How do I create a procedure? First we created was a process that makes the value of r can menjasi pangakat accordance with the tribe. After that we created a new loop that prints the value of each array geometry. Step tersakhir ie summing series.
In the picture below procedure, the process may be in the red box and inside the green box is the process of printing spare geometry.

Matrix Symmetry: Program to Check a Matrix Symmetry

This time I will discuss about the matrix symmetry.

Box matrix A is called symmetric if A = AT
Examples of symmetric matrices:



Theorem :
If A and B are symmetric matrices with the same size, and if k is a scalar then AT is a symmetric A + B and A - B is symmetrical kA is symmetrical (AB) T = BTAT = BA

If A is a symmetric matrix that can be in inverse, then A - 1 is a symmetric matrix.
Assume that A is a symmetric matrix and can be in the inverse, that A = AT, then:
(A − 1)T = (AT) − 1 = A − 1
Yang mana membuktikan bahwa A − 1 adalah simetris.

Produk AAT dan ATA
(AAT)T = (AT)TAT = AAT dan (ATA)T = AT(AT)T = ATA
Contoh
A adalah matriks 2 X 3
Which proves that A - 1 is symmetric.

AAT and ATA Products

(AAT) T = (AT) TAT = AAT and (ATA) T = AT (AT) T = ATA
Examples
A is the matrix 2 X 3 :


If A is a matrix that can be in inverse, then the AAT and ATA also be in inverse.

With the above understanding we can create a program to determine a metric symmetry or not. As the procedure can we make something like this:

To better understand the more there is a program that I have prepared to try using the Dev-C + +

Join The Set: The Multiplication On The Set

This time we will discuss the multiplication on the set or the more frequently heard hipunan join. Multiple purpose here is not like multiplying 2 x 3 = 5, but we are combining two or more sets.

For example we have set A and B, A × B means the set of all ordered pairs with the first element of each pair selected from A and the second element selected from B.

Example:
A: {1,2,3} and B: {a, b, c},
then A x B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c), (3, a), (3 , b), (3, c)}

After getting the process that occurs over and over - again we can make a program using nested loops. That loop is in the loop. I made ​​it like this:

Searching (Array One Dimension) : Finding a Number From Several Numbers

Still talking one-dimensional array problem. In the array much to do kit. From the most minor sort the numbers to the greatest or from greatest to smallest. Also we will discuss this time is to find a number of the many numbers entered.


For example there is input data 5, 6, 2, 4, 8. 5 will automatically be stored in the array index of 1, 6 will be stored in the array index 2, 2 will be stored in the array index of 3, 4 will be stored in the array index 4, 8 will be stored in the array index 5, with our record array indices start from 1 . Because the default array index starts from 0.


Because there is an array index we can find a number that is located on an array index. As an example we look for number 2. Algorithm that is where all the numbers look the same with blangan to be searched. If you've met the index of an array of printing as a result of the position of the storage array. So number 2 is located at position 3 of a series that included bilagan.


The program can be created like this :