Sum of the series 0.6, 0.06, 0.006, 0.0006, …to n terms

Given the number of terms i.e. n. Find the sum of the series 0.6, 0.06, 0.006, 0.0006, …to n terms.

Examples:

Input : 2
Output : 0.65934

Input : 3
Output : 0.665334



Lets denote the sum by S:
Using the formula S_{n}=\frac{a\left ( 1-r^{n} \right )}{1-r}, we have [since r<1]

S_{n}=\frac{\frac{6}{10}\left \{ 1-\left ( \frac{1}{10} \right )^n\right \}}{1-\frac{1}{10}}

S_{n}=\frac{6}{9}\left ( 1-\frac{1}{10^n} \right )

S_{n}=\frac{2}{3}\left ( 1-\frac{1}{10^n} \right )

Hence the required sum is S_{n}=\frac{2}{3}\left ( 1-\frac{1}{10^n} \right )

Below is the implementation:

C++

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// CPP program to find sum of 0.6, 0.06,
// 0.006, 0.0006, ...to n terms
#include <bits/stdc++.h>
using namespace std;
  
// function which return the
// the sum of series
float sumOfSeries(int n)
{
    return (0.666) * (1 - 1 / pow(10, n));
}
  
// Driver code
int main()
{
    int n = 2;
    cout << sumOfSeries(n);
}

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Java














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// java program to find sum of 0.6, 0.06, 


// 0.006, 0.0006, ...to n terms 


import java.io.*; 


  


class GFG  


{ 


    // function which return the 


    // the sum of series 


    static double sumOfSeries(int n) 


    { 


        return (0.666) * (1 - 1 /Math. pow(10, n)); 


    } 


      


      


    // Driver code 


    public static void main (String[] args)  


    { 


        int n = 2; 


        System.out.println ( sumOfSeries(n)); 


          


    } 


} 


  


// This code is contributed by vt_m 



















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Python3














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# Python3 program to find  


# sum of 0.6, 0.06, 0.006,  


# 0.0006, ...to n terms 


import math 


  


# function which return  


# the sum of series 


def sumOfSeries(n): 


    return ((0.666) * 


            (1 - 1 / pow(10, n))); 


  


# Driver code 


n = 2; 


print(sumOfSeries(n)); 


  


# This code is contributed by mits 



















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C#














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// C# program to find sum of 0.6, 0.06, 


// 0.006, 0.0006, ...to n terms 


using System; 


  


class GFG { 


      


    // function which return the 


    // the sum of series 


    static double sumOfSeries(int n) 


    { 


        return (0.666) * (1 - 1 /Math. Pow(10, n)); 


    } 


      


    // Driver code 


    public static void Main ()  


    { 


        int n = 2; 


          


        Console.WriteLine( sumOfSeries(n)); 


          


    } 


} 


  


// This code is contributed by vt_m 



















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PHP














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<?php 


// PHP program to find sum of 0.6, 0.06, 


// 0.006, 0.0006, ...to n terms 


  


// function which return the 


// the sum of series 


function sumOfSeries($n) 


{ 


    return (0.666) * (1 - 1 /  


                pow(10, $n)); 


} 


  


// Driver code 


$n = 2; 


echo(sumOfSeries($n)); 


  


// This code is contributed by Ajit. 


?> 



















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Output:


0.65934




          
          
          

          

    

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