# Sum of the series 1, 2, 4, 3, 5, 7, 9, 6, 8, 10, 11, 13.. till N-th term

Given a series of numbers 1, 2, 4, 3, 5, 7, 9, 6, 8, 10, 11, 13… The task is to find the sum of all the numbers in series till N-th number.

Examples:

Input: N = 4
Output: 10
1 + 2 + 4 + 3 = 10

Input: N = 10
Output: 55

Approach: The series is basically 20 odd numbers, 21 even numbers, 22 even numbers…. The sum of first N odd numbers is N * N and sum of first N even numbers is (N * (N+1)). Calculate the summation for 2i odd or even numbers and keep adding them to the sum.

Iterate for every power of 2, till the number of iterations exceeds N, and keep adding the respective summation of odd or even numbers according to the parity. For every segment the sum of the segment will be, (current sum of X odd/even numbers – previous sum of Y odd/even numbers), where X is the total sum of odd/even numbers till this segment and Y is the summation of odd/even numbers till the previous when odd/even numbers occurred.

Below is the implementation of the above approach:

## C++

 // C++ program to implement // the above approach    #include using namespace std;    // Function to find the // sum of first N odd numbers int sumodd(int n) {     return (n * n); }    // Function to find the // sum of first N even numbers int sumeven(int n) {     return (n * (n + 1)); }    // Function to overall // find the sum of series int findSum(int num) {        // Initiall odd numbers     int sumo = 0;        // Initial even numbers     int sume = 0;        // First power of 2     int x = 1;        // Check for parity     // for odd/even     int cur = 0;        // Counts the sum     int ans = 0;     while (num > 0) {            // Get the minimum         // out of remaining num         // or power of 2         int inc = min(x, num);            // Decrease that much numbers         // from num         num -= inc;            // If the segment has odd numbers         if (cur == 0) {                // Summate the odd numbers             // By exclusion             ans = ans + sumodd(sumo + inc) - sumodd(sumo);                // Increase number of odd numbers             sumo += inc;         }         // If the segment has evn numbers         else {                // Summate the even numbers             // By exclusion             ans = ans + sumeven(sume + inc) - sumeven(sume);                // Increase number of even numbers             sume += inc;         }            // Next set of numbers         x *= 2;            // Change parity for odd/even         cur ^= 1;     }        return ans; }    // Driver code int main() {     int n = 4;     cout << findSum(n);        return 0; }

## Java

 // Java program to implement // the above approach    class GFG {        // Function to find the     // sum of first N odd numbers     static int sumodd(int n)     {         return (n * n);     }        // Function to find the     // sum of first N even numbers     static int sumeven(int n)     {         return (n * (n + 1));     }        // Function to overall     // find the sum of series     static int findSum(int num)      {            // Initiall odd numbers         int sumo = 0;            // Initial even numbers         int sume = 0;            // First power of 2         int x = 1;            // Check for parity         // for odd/even         int cur = 0;            // Counts the sum         int ans = 0;         while (num > 0)          {                // Get the minimum             // out of remaining num             // or power of 2             int inc = Math.min(x, num);                // Decrease that much numbers             // from num             num -= inc;                // If the segment has odd numbers             if (cur == 0)             {                    // Summate the odd numbers                 // By exclusion                 ans = ans + sumodd(sumo + inc) - sumodd(sumo);                    // Increase number of odd numbers                 sumo += inc;             }                             // If the segment has evn numbers             else             {                    // Summate the even numbers                 // By exclusion                 ans = ans + sumeven(sume + inc) - sumeven(sume);                    // Increase number of even numbers                 sume += inc;             }                // Next set of numbers             x *= 2;                // Change parity for odd/even             cur ^= 1;         }            return ans;     }        // Driver code     public static void main(String[] args)      {         int n = 4;         System.out.println(findSum(n));        } }    // This code contributed by Rajput-Ji

## Python

 # Python3 program to implement # the above approach    # Function to find the # sum of first N odd numbers def sumodd(n):        return (n * n)    # Function to find the # sum of first N even numbers def sumeven(n):        return (n * (n + 1))       # Function to overall # find the sum of series def findSum(num):           # Initiall odd numbers     sumo = 0        # Initial even numbers     sume = 0        # First power of 2     x = 1        # Check for parity     # for odd/even     cur = 0        # Counts the sum     ans = 0     while (num > 0):            # Get the minimum         # out of remaining num         # or power of 2         inc = min(x, num)            # Decrease that much numbers         # from num         num -= inc            # If the segment has odd numbers         if (cur == 0):                # Summate the odd numbers             # By exclusion             ans = ans + sumodd(sumo + inc) - sumodd(sumo)                # Increase number of odd numbers             sumo += inc                    # If the segment has evn numbers         else:                # Summate the even numbers             # By exclusion             ans = ans + sumeven(sume + inc) - sumeven(sume)                # Increase number of even numbers             sume += inc                       # Next set of numbers         x *= 2            # Change parity for odd/even         cur ^= 1            return ans    # Driver code n = 4 print(findSum(n))    # This code is contributed by mohit kumar

## C#

 // C# program to implement // the above approach using System;    class GFG {        // Function to find the     // sum of first N odd numbers     static int sumodd(int n)     {         return (n * n);     }        // Function to find the     // sum of first N even numbers     static int sumeven(int n)     {         return (n * (n + 1));     }        // Function to overall     // find the sum of series     static int findSum(int num)      {            // Initiall odd numbers         int sumo = 0;            // Initial even numbers         int sume = 0;            // First power of 2         int x = 1;            // Check for parity         // for odd/even         int cur = 0;            // Counts the sum         int ans = 0;         while (num > 0)          {                // Get the minimum             // out of remaining num             // or power of 2             int inc = Math.Min(x, num);                // Decrease that much numbers             // from num             num -= inc;                // If the segment has odd numbers             if (cur == 0)             {                    // Summate the odd numbers                 // By exclusion                 ans = ans + sumodd(sumo + inc) - sumodd(sumo);                    // Increase number of odd numbers                 sumo += inc;             }                             // If the segment has evn numbers             else             {                    // Summate the even numbers                 // By exclusion                 ans = ans + sumeven(sume + inc) - sumeven(sume);                    // Increase number of even numbers                 sume += inc;             }                // Next set of numbers             x *= 2;                // Change parity for odd/even             cur ^= 1;         }            return ans;     }        // Driver code     public static void Main(String[] args)      {         int n = 4;         Console.WriteLine(findSum(n));        } }    // This code has been contributed by 29AjayKumar

## PHP

 0)      {            // Get the minimum         // out of remaining num         // or power of 2         \$inc = min(\$x, \$num);            // Decrease that much numbers         // from num         \$num -= \$inc;            // If the segment has odd numbers         if (\$cur == 0)         {                // Summate the odd numbers             // By exclusion             \$ans = \$ans + sumodd(\$sumo + \$inc) -                            sumodd(\$sumo);                // Increase number of odd numbers             \$sumo += \$inc;         }                    // If the segment has evn numbers         else          {                // Summate the even numbers             // By exclusion             \$ans = \$ans + sumeven(\$sume + \$inc) -                            sumeven(\$sume);                // Increase number of even numbers             \$sume += \$inc;         }            // Next set of numbers         \$x *= 2;            // Change parity for odd/even         \$cur ^= 1;     }        return \$ans; }    // Driver code \$n = 4; echo findSum(\$n);    // This code contributed by princiraj1992 ?>

Output:

10

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Striver(underscore)79 at Codechef and codeforces D

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