Number Series Codes Using C#

Introduction

This article is a continuation of Number series.

To set up the environment for C# in visual studio code or read more number series, please refer to my previous article Number Series Codes using C#.

Geometric Progression Series (G. P)

The general form of a GP is a, ar, ar2, ar3 and so on. The nth term of a GP series is Tn = arn-1, where a = first term and r = common ratio = Tn/Tn-1) .

The sum of infinite terms of a GP series S∞= a/(1-r) where 0< r<1. If a is the first term, r is the common ratio of a finite G.P.

G.P series calculated using formula {a, ar, ar2, ar3, ... } where a is first number and r is common ration

//print the sum of Geometric Progresson
public void GPSeries()
{
// The general form of a GP is a, ar, ar2, ar3 and so on. The nth term of a GP series is Tn = arn-1, where a = first term and r = common ratio = Tn/Tn-1) .
// The sum of infinite terms of a GP series S∞= a/(1-r) where 0< r<1. If a is the first term, r is the common ratio of a finite G.P.
// suppose first number = 1, terms = 5, common ratio = 2
// Number of G.P Series are 1, 2, 4, 8, 16, 32
// The sum of the G.P series: 32 {a, ar, ar2, ar3, ... } where a is first number and r is common ration
double gProgess = 0, sum = 0;
Console.Write("Enter the first number: ");
int firstNum = Convert.ToInt32(Console.ReadLine()); // read the first number and save into firstNum variable
Console.Write("Enter the number or terms: ");
int nTerm = Convert.ToInt32(Console.ReadLine()); // read the terms
Console.Write("Enter the common ratio : ");
int ratio = Convert.ToInt32(Console.ReadLine()); // read the common ratio
int firstValue = 1; // initialize the first value
Console.Write("Number for the G.P Series:");
Console.Write(firstValue + " "); // print first value.
for (int i = 1; i <= nTerm; i++) // loop till nTerm.
{
gProgess = Math.Pow(ratio, i); // find the g.p progression
Console.Write("{0} ", gProgess); // print the progression
}
sum = (firstNum * (1 - (Math.Pow(ratio, nTerm + 1)))) / (1 - ratio); // calculate the sum and save into variable sum.
double term = firstNum * (Math.Pow(ratio, nTerm - 1)); // calculate the term and store into variable term.
Console.Write("\nThe tn terms of G.P. : {0}\n\n", term); // print the term.
Console.Write("\nThe Sum of the G.P. series : {0}\n\n", sum);// print the sum.
}

Output

Arithmetic Progression Series (A. P)

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

A.P series with common difference of 3 for 10 items is {1 , 4, 7, 10, 13, 16, 19 , 22, 25, 28}

// Print sum of Arithmetic Progression(A.P) series
public void printAPSeries()
{
//An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
// A.P series with common difference of 3 for 10 items is {1 , 4, 7, 10, 13, 16, 19 , 22, 25, 28}
// Sum of Above series is = 145
Console.Write("Enter the starting number: ");
int startNum = Convert.ToInt32(Console.ReadLine()); // read items
Console.Write("Enter the number of items: ");
int items = Convert.ToInt32(Console.ReadLine()); // read items
Console.Write("Enter the common difference: ");
int diff = Convert.ToInt32(Console.ReadLine()); // read difference number
int sum = (items * (2 * startNum + (items - 1) * diff)) / 2; // calculate the sum
int lastNum = startNum + (items - 1) * diff; // calculate the new last number
Console.Write("\nThe Sum of the A.P. series are : \n");
for (int i = startNum; i <= lastNum; i = i + diff)
{
if (i != lastNum)
{
Console.Write("{0} + ", i);
}
else
{
Console.Write("{0} = {1} \n\n", i, sum);
}
}
}

Output

Strong Number

A strong number is a special number whose sum of the factorial of digits is equal to the original number.

// check whether a number is Strong Number or not.
public void CheckStrongNumber()
{
// Strong number is a special number whose sum of factorial of digits is equal to the original number.
// Suppose input number is 145
// Factorial of digita of input numbers is 1 = 1, 4 = 24 , 5 = 120
// Sum of factorial number is: 1 + 24 + 120 = 145
// Hence the input number 145 is a armstrong number.
Console.Write("Enter the number: ");
int number = Convert.ToInt32(Console.ReadLine()); // read number
int fact, temp, sum = 0, digit, i;
temp = number; // save the original number to temp variable.
Console.Write("Factorial of digits: ");
for (i = number; i > 0; i = i / 10) // divide the input number by 10
{
fact = 1;
for (digit = 1; digit <= i % 10; digit++) // To get digit from number perform number % 10;
{
fact = fact * digit; // Calculate the factorial of given digits.
}
Console.Write("{0} = {1}", digit - 1, fact + ", "); // print the factorial fo digits
sum = sum + fact; // Add the factorial of digits.
}
Console.WriteLine("");
Console.Write("sum of factorial of digits: " + sum);
Console.WriteLine("");
if (sum == temp) // check sum of factorial of digits is equal to input number.
{
Console.Write(temp + " is a Strong number"); // If yes, then input number is strong number
}
else
{
Console.Write(temp + " is a Strong number");// else it is not strong number.
}
}

Output

Pascal's Triangle

The Pascal's triangle is a triangular array of binomial coefficients.

// print pascal triangle for given range
public void PascalTriangle()
{
// 1
// 1 1
// 1 2 1
Console.Write("Enter the number of rows: ");
int number = Convert.ToInt32(Console.ReadLine()); // read number of rows
int space, rows, cols, pasDigit = 1;
for (rows = 0; rows < number; rows++) // loop each rows
{
for (space = 1; space < number - rows; space++) // this loop for printing space number - rows;
{
Console.Write(" ");
}
for (cols = 0; cols <= rows; cols++) // loops each cols
{
if (cols == 0 || rows == 0) // check rows or cols value is 0.
{
pasDigit = 1; // if yes pasDigit will be 1;
}
else
{
pasDigit = pasDigit * (rows - cols + 1) / cols; // else pasDigit = pasDigit * (row -cols + 1) / cols;
}
Console.Write(pasDigit + " ");
}
Console.WriteLine("");
}
}

Output

Armstrong Number

The sum of the cube of the digit of input number equal to the input number is called an Armstrong number.

//check Armstrong number
public void ArmStrongNumber()
{
// sum of the cube of digit of input number equal to input number is called armstrong number.
// Suppose the input number is 153
// Cube of digit number 1 = 1, 5 = 125 , 3 = 27
// Sum of cube = 1 + 125 + 27 = 153
// Hence the input number 153 is armstrong number.
Console.Write("Enter the number: ");
int number = Convert.ToInt32(Console.ReadLine()); // read the number
int sum = 0; // initialize with 0
int temp;
int digit;
Console.Write("Cube of digit of the enter number:");
for (temp = number; number != 0; number = number / 10) // divide the number by 10
{
digit = number % 10; // find the digit for given number
Console.Write(digit * digit * digit + " "); // print the cube of digit
sum = sum + (digit * +digit * digit); // Add and store the cube of digit
}
Console.WriteLine("");
Console.Write("Sum of digits of enter number: " + sum); // print the sum of armstrong number
Console.WriteLine("");
if (sum == temp) // check given number and sum of armstrong number is equal
{
Console.Write(temp + " is ArmStrong Number"); // If yes then it is armstrong number
}
else
{
Console.Write(temp + " is not ArmStrong Number"); // else it is not a armstrong number
}
}

Output

Perfect Number

A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself.

// check perfect number or not
public void PerfectNumber()
{
// A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself
// Suppose Input number is 28
// Positive divisor excluding 28 is = 1 2 4 7 14
// Sum of Positive divisor = 1 + 2 + 4 + 7 + 14 = 28
// Hence 28 is a perfect number.
Console.Write("Enter the number: ");
int number = Convert.ToInt32(Console.ReadLine()); // read the number
int sum = 0; // initialize with 0
Console.Write("Number is divisible by: ");
for (int i = 1; i < number; i++) // check number less than given number
{
if (number % i == 0) // check given number is divisible by how many number.
{
Console.Write(i + " "); // print the perfect divisor
sum += i; // add number which divide the given number
}
}
Console.WriteLine("");
Console.Write("Sum of perfect divisor is :" + sum);
Console.WriteLine("");
if (sum == number)// check sum and original number.
{
Console.Write(number + " is a perfect number");
}
else
{
Console.Write(number + " is not a perfect number");
}
}

Output

Natural Number

The natural numbers are a part of the number system which includes all the positive integers from 1 to infinity.

It is always greater than zero

//Print the n terms of square natural number and their sum without function.
public void NaturalNumberSquare()
{ // Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity.
// It is always greater than zero
// Example of natural number is 1, 2, 3........infinity.
Console.Write("Enter the number of natural number: ");
int number = Convert.ToInt32(Console.ReadLine()); // read n number of natural number
int sum = 0; // initialize sum value
for (int i = 1; i <= number; i++) // loop each natural number
{
Console.Write(" " + i * i + " "); // print the square of natural number
sum += i * i; // Add the square of natural number
}
Console.WriteLine("");
Console.Write("Sum of square of natural number upto {0} term: {1}", number, sum);
}

Output

Print Floyd's Triangle

Floyd's triangle is a right-angled triangular array of natural numbers.

//print the Floyd's Triangle.
public void FloydTriangle()
{
// Floyd's triangle is a right-angled triangular array of natural numbers
Console.Write("Enter the number of rows: ");
int number = Convert.ToInt32(Console.ReadLine()); // read number of rows
int a, b; // declare two temperary variable
for (int rows = 1; rows <= number; rows++)
{
if (rows % 2 == 0) // check number is divisible by 2. If divisible set a=1 and b=0
{
a = 1;
b = 0;
}
else // else reverse the value of a and b.
{
a = 0;
b = 1;
}
for (int cols = 1; cols <= rows; cols++) // loops to handle each cols value
{
if (cols % 2 == 0) // check number is divisible by 2
{
Console.Write(" " + a); // if yes print a value
}
else // else b value
{
Console.Write(" " + b);
}
}
Console.WriteLine("");
}
}

Output

Sum of Series

Print the sum of series [2+ 22 + 222 + 2222 + ...]

// Print the sum of series [ 2 + 22 + 222 + 2222 + 22222 ...].
public void SumOfSeries()
{
Console.Write("Enter the term value: ");
int term = Convert.ToInt32(Console.ReadLine()); // read the term value
Console.Write("Enter the number of term: ");
int num = Convert.ToInt32(Console.ReadLine()); // read the number of term
int sum = 0;
int actualTerm = term;
for (int i = 0; i < num; i++) // loop the number of term
{
Console.Write(" " + term); // print the term
sum += term; // add the term and store into variable sum
term = term * 10 + actualTerm; // miltiply the term wih 10 and add the term i.e 2 2*10+2 22*10+2 222*10+2
}
Console.WriteLine("");
Console.Write("Sum of series: " + sum);
}

Output

Print Pattern increased by one

Print the pattern like a right-angle triangle, with the number increased by 1.

//Print pattern like right angle triangle with number increased by 1
public void TrianglePatternIncreasedByOne()
{
Console.Write("Enter the number or rows: ");
int number = Convert.ToInt32(Console.ReadLine()); // read number of rows
int rows, cols, printNum = 1;
for (rows = 0; rows <= number; rows++) // this loops will handle the rows condition
{
for (cols = 0; cols < rows; cols++) // this loops will handle the column condition
{
Console.Write(printNum++ + " "); // print the number and increment it by 1
}
Console.WriteLine(" ");
}
}

Output

Print Pyramid increased by one

Print the pyramid with the number increased by 1.

// print pattern like pyramid with number increased by 1
public void PyramidPatternIncreadByOne()
{
Console.Write("Enter the number or rows: ");
int number = Convert.ToInt32(Console.ReadLine()); // read number of rows
int rows, cols, temp, space = number, printNum = 1;
for (rows = 0; rows <= number; rows++)
{
for (cols = space; cols >= 1; cols--) // print spaces
{
Console.Write(" ");
}
for (temp = 1; temp <= rows; temp++) // print number of value in rows
{
Console.Write(printNum++ + " ");
}
Console.WriteLine(" "); // enter new line and print space
space--; // decrement the space by one
}
}
}

Output

You can download the solution from the attachment.