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

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

1², (1²+2²), (1²+2²+3²),….,till N terms

Examples:

Input: N = 3

Output: 20

Input: N = 1

Output: 1

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

Given 1^2, (1^2+2^2), (1^2+2^2+3^2),….,till N terms

S_N = N * (N+1)² * (N+2) / 12

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+1)*(N+2)/12;

}

// Driver Code

int main()
{
    int N = 3;

    cout << findSum(N);
}

Java

// Java program to implement
// the above approach

class GFG {

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

    static int findSum(int N) {

        return N * (N + 1) * (N + 1) * (N + 2) / 12;

    }

    // Driver Code

    public static void main(String args[]) {
        int N = 3;

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

// This code is contributed by Saurabh Jaiswal

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+1)*(N+2)//12


# Driver Code
if __name__ == "__main__":

    # Value of N
    N = 3
    print(findSum(N))

# This code is contributed by Abhishek Thakur.

C#

// C# program to implement
// the above approach
using System;
class GFG
{

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

static int findSum(int N){

  return N*(N+1)*(N+1)*(N+2)/12;

}

// Driver Code

public static void Main()
{
    int N = 3;

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

// This code is contributed by Samim Hossain Mondal.

Javascript

<script>
// 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+1)*(N+2)/12;

}

// Driver Code

let N = 3;
document.write(findSum(N));

// This code is contributed by Samim Hossain Mondal.
</script>

Output

20

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