CBSE Class 11 - Computer Science - Simple C++ Snippets (Part-4)

Sequence & Series

Q1: Write a program to to find the sum of series as:
        S = 1² + 2² + 3² + ... + n²

Answer:

// program to find sum of series
// S = 1^2 + 3^2 + 5^2 + ... + n^2
//
#include <iostream.h>
#include <conio.h>
#include <manip.h>

int main()
{
  clrscr();             // clear the screen
  unsigned int n;
  unsigned long sum;
  clrscr();
  cout << "Enter range(n) = ";
  cin >> n;
  sum = 0;
  cout << "S = ";
  for (int i = 1; i <= n; i=i+2)
    {
     cout << i << "^" << 2;
     if (i < n)
       cout << " + ";
     sum += i*i;
    }
  cout << "\nSum = " << sum << endl;
  getch();
  return 0;
}

The program will have the following output:

Q2: Write a program to sum the following sequence?
              S = x + x²/2 + x³/3 + x⁴/4 +... + xⁿ/n


Answer:

// program to sum the following sequence
// x + x^2/2 + x^3/3 + x^4/4 + ... + x^n/n
//
#include <iostream.h>
#include <conio.h>
#include <math.h>

int main()
{
  clrscr();             // clear the screen
  int x,n;
  float sum = 0.0;
  clrscr();
  cout << "Enter the value of x= ";
  cin >> x;
  cout << "Enter the value of n= ";
  cin >> n;

  for (int i = 1; i <=n; ++i)
  {
    if (i == 1)
      {
       sum = x;
       continue;
      }
    sum += ((float)pow(x,i)/(float)i);
  }
  cout << "Sum=" << sum;
  getch();
  return 0;
}

Q3: Write a program to find the sum of the following sequence:
              S = x - x²/2! + x³/3! - x⁴/4! +x⁵/5! - x⁶/6!

Answer:

// program to find sum the following sequence
// x - x^2/2! + x^3/3! - x^4/4! + x^5/5! - x^6/6!
//
#include <iostream.h>
#include <conio.h>
#include <math.h>

int main()
{
  clrscr();             // clear the screen
  int x, k;
  double sum = 0.0;
  cout << "Enter the value of x= ";
  cin >> x;
  k = -1;

  for (int i = 1; i <=6; ++i)
   {
    k = k * -1;
    if (i == 1)
     {
      sum = x;
      continue;
     }
    // calculate factorial
    double fact = 1.0;
    for (int j = 1; j <= i; ++j)
     {
      fact *= j;
     }
    sum += ((double)pow(x,i)/fact)*k;
   }
  cout << "Sum=" << sum;
  getch();
  return 0;
}

The program will have the following output:

Q4: Write a program to print the first 10 Fibonacci numbers.

Answer:

// program to find sum the following sequence
// write a program to print first 10 Fibonacci numbers
//
#include <iostream.h>
#include <conio.h>

int main()
{
  int n1, n2, n3;
  n1 = 0;
  n2 = 1;
  // clear screen
  clrscr();
  for (int i = 0; i < 10; ++i)
  {
    // print first two fibonacci numbers
    if (i == 0)
     cout << n1;
    else if (i == 1)
     cout << n2;
    else
     {
      // compute next fibonacci number
      n3 = n1 + n2;
      cout << n3;
      n1 = n2;
      n2 = n3;
     }
     cout << "  ";
  }
  getch();
  return 0;
}

The program will have the following output:

Q5: Write a  c++ program to input integers in an array of  size 10. Find the sum of even numbers in that array.

Answer:

// wap to input an integer array of size 10
// and find the sum of even numbers in an array
//
#include <iostream.h>
#include <conio.h>

int main()
{
  int arr[10];
  int i;
  clrscr();
  cout << "Enter 10 integers\n";
  for (i = 0; i < 10; ++i)
  {
    cout << "Enter number [" << i+1 << "]=";
    cin >> arr[i];
  }
  // compute sum of even numbers
  long sum = 0;
  int evens = 0;
  for (i = 0; i < 10; ++i)
  {
      // check if number is even, then add
      if (arr[i] % 2 == 0)
      {
  sum += arr[i];
  evens++;
      }
  }
  cout << "There are " << evens << " evens and their sum=" << sum << endl;
  getch();
  return 0;
}

Q6: Write a program to find the sum of digits. 
e.g. if number entered is 2374, S = 2+3+7+4 = 16

Answer:

// program to find the sum of a number
// e.g. 123, sum = 1 + 2 + 3
//
#include <iostream.h>
#include <conio.h>

int main()
{
    unsigned int num, digit;
    clrscr();
    cout << "Enter an integer number:";
    cin >> num;
    long sum = 0;
    cout << "Sum of digits:" << num << "\n";
    while (num > 0)
    {
      digit = num % 10;
      sum = sum + digit;
      num = num / 10;
      cout << digit << "+";
    }
    cout << "=" << sum << endl;
  getch();
  return 0;
}

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