# Sum of the first N terms of the series 2,10, 30, 68,….

• Last Updated : 31 May, 2022

Given a number N, the task is to find the sum of first N terms of the below series:

Sn = 2 + 10 + 30 + 68 + … upto n terms

Examples:

Input: N = 2
Output: 12
2 + 10
= 12

Input: N = 4
Output: 40
2 + 10 + 30 + 68
= 110

Approach: Let, the nth term be denoted by tn.
This problem can easily be solved by splitting each term as follows :

Sn = 2 + 10 + 30 + 68 + ......
Sn = (1+1^3) + (2+2^3) + (3+3^3) + (4+4^3) +......
Sn = (1 + 2 + 3 + 4 + ...unto n terms) + (1^3 + 2^3 + 3^3 + 4^3 + ...upto n terms)

We observed that Sn can broken down into summation of two series.
Hence, the sum of first n terms is given as follows:

Sn = (1 + 2 + 3 + 4 + ...unto n terms) + (1^3 + 2^3 + 3^3 + 4^3 + ...upto n terms)
Sn = n*(n + 1)/2 + (n*(n + 1)/2)^2

Below is the implementation of above approach:

## C++

 // C++ program to find sum of first n terms#include using namespace std; // Function to calculate the sumint calculateSum(int n){     return n * (n + 1) / 2           + pow((n * (n + 1) / 2), 2);} // Driver codeint main(){    // number of terms to be    // included in the sum    int n = 3;     // find the Sum    cout << "Sum = " << calculateSum(n);     return 0;}

## Java

 // Java program to find sum of first n terms public class GFG {         // Function to calculate the sum    static int calculateSum(int n)    {               return n * (n + 1) / 2                + (int)Math.pow((n * (n + 1) / 2), 2);    }         // Driver code    public static void main(String args[])    {        // number of terms to be        // included in the sum        int n = 3;               // find the Sum        System.out.println("Sum = "+ calculateSum(n));    }    // This Code is contributed by ANKITRAI1}

## Python3

 # Python program to find sum# of first n terms # Function to calculate the sumdef calculateSum(n):    return (n * (n + 1) // 2 +        pow((n * (n + 1) // 2), 2)) # Driver code # number of terms to be# included in the sumn = 3 # find the Sumprint("Sum = ", calculateSum(n)) # This code is contributed by# Sanjit_Prasad

## C#

 // C# program to find sum of first n termsusing System;class gfg{    // Function to calculate the sum    public void calculateSum(int n)    {        double r = (n * (n + 1) / 2 +                Math.Pow((n * (n + 1) / 2), 2));        Console.WriteLine("Sum = " + r);    }     // Driver code    public static int Main()    {        gfg g = new gfg();         // number of terms to be        // included in the sum        int n = 3;                 // find the Sum        g.calculateSum(n);        Console.Read();        return 0;    }}



## Javascript



Output:

Sum = 42

Time Complexity: O(1), the code will run in a constant time.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

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