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Find sum of the series ?3 + ?12 +……… upto N terms
  • Last Updated : 12 Oct, 2018

Given a number n, the task is to find the sum of first n terms of this series. Below is the series:

     $$\sqrt{3}+\sqrt{12}+\sqrt{27}+\sqrt{48}+\sqrt{75}+\cdots$$

Examples:

Input: n = 10
Output: 95.2628

Input: n = 5
Output: 25.9808

This series can be seen as-

     $$1\sqrt{3}+2\sqrt{3}+3\sqrt{3}+4\sqrt{3}+5\sqrt{3}+\cdots$$ Now, take $\sqrt{3} $ as common, we get- $$\sqrt{3}\left[1+2+3+4+5+\cdots\right]$$ $$sum=\sqrt{3}*\left(\frac{n*(n+1)}{2}\right)$$



Below is the required implementation:

C++




// C++ implementation of above approach
#include <bits/stdc++.h>
#define ll long long int
using namespace std;
  
// Function to find the sum
double findSum(ll n)
{
  
    // Apply AP formula
    return sqrt(3) * (n * (n + 1) / 2);
}
// Driver code
int main()
{
    // number of terms
    ll n = 10;
  
    cout << findSum(n) << endl;
    return 0;
}


Java




// Java implementation of 
// above approach
import java.io.*;
  
class GFG 
{
  
// Function to find the sum
static double findSum(long n)
{
    // Apply AP formula
    return Math.sqrt(3) * (n * 
                    (n + 1) / 2);
}
// Driver code
public static void main (String[] args) 
{
    // number of terms
    long n = 10;
      
    System.out.println( findSum(n));
}
}
  
// This code is contributed 
// by inder_verma..


Python3




# Python3 implementation of above approach
  
#Function to find the sum
import math
def findSum(n):
    # Apply AP formula
    return math.sqrt(3) * (n * (n + 1) / 2)
  
# Driver code 
# number of terms
if __name__=='__main__':
    n = 10
    print(findSum(n))
  
# This code is contributed by sahilshelangia


C#




// C# implementation of 
// above approach
using System;
  
class GFG 
{
  
// Function to find the sum
static double findSum(long n)
{
    // Apply AP formula
    return Math.Sqrt(3) * (n * 
                    (n + 1) / 2);
}
// Driver code
public static void Main () 
{
    // number of terms
    long n = 10;
      
    Console.WriteLine( findSum(n));
}
}
  
// This code is contributed 
// by inder_verma..


PHP




<?php
// PHP implementation of above approach
  
// Function to find the sum
function findSum($n)
{
  
    // Apply AP formula
    return sqrt(3) * ($n * ($n + 1) / 2);
}
  
// Driver code
  
// number of terms
$n = 10;
  
echo findSum($n);
  
// This code is contributed 
// by inder_verma
?>


Output:

95.2628

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