Find the sum of N terms of the series 1, (2+3), (4+5+6), …..

Given a positive integer, N. Find the sum of the first N term of the series-

1, (2+3), (4+5+6),….,till N terms

Examples:

Input: N = 5

Output: 120

Input: N = 1

Output: 1

Approach: The sequence is formed by using the following pattern. For any value N-

S_N = N * (N + 1) * (N² + N + 2) / 8

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to return sum of
// N term of the series

int findSum(int N)
{

    return N
      * (N + 1)
      * (N * N + N + 2) / 8;
}

// Driver Code
int main()
{
    int N = 5;

    cout << findSum(N);
}

Java

/*package whatever //do not write package name here */

import java.io.*;

class GFG {

    // Function to return sum of
    // N term of the series
    static int findSum(int N)
    {

        return N * (N + 1) * (N * N + N + 2) / 8;
    }

    // Driver Code
    public static void main(String[] args)
    {
        int N = 5;

        System.out.println(findSum(N));
    }
}

// This code is contributed by Potta Lokesh

Python3

# Python 3 program for the above approach

# Function to return sum of
# N term of the series

def findSum(N):
    return N * (N + 1) * (N * N + N + 2) // 8


# Driver Code
if __name__ == "__main__":

    # Value of N
    N = 5
    print(findSum(N))

# This code is contributed by Abhishek Thakur.

C#

/*package whatever //do not write package name here */
using System;

class GFG
{

  // Function to return sum of
  // N term of the series
  static int findSum(int N)
  {

    return N * (N + 1) * (N * N + N + 2) / 8;
  }

  // Driver Code
  public static void Main()
  {
    int N = 5;

    Console.Write(findSum(N));
  }
}

// This code is contributed by Saurabh Jaiswal

Javascript

// Javascript program to implement
// the above approach

// Function to return sum of
// N term of the series
function findSum(N)
{

    return N
      * (N + 1)
      * (N * N + N + 2) / 8;
}

// Driver Code
let N = 5
document.write(findSum(N))

// This code is contributed by saurabh_jaiswal.

Output

120

Time Complexity: O(1), since there is no loop or recursion.
Auxiliary Space: O(1), since no extra space has been taken.