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++

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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);
}

chevron_right






                        filter_none









Java














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// 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 



















                        chevron_right







                        filter_none









Python3














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















# 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 



















                        chevron_right







                        filter_none









C#














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// 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 



















                        chevron_right







                        filter_none









PHP














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















<?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. 


?> 



















                        chevron_right







                        filter_none










Output:


0.65934




          
          
          
          

            

    

        My Personal Notes
        arrow_drop_up
    

    

        
        

            
            
        

    


Recommended Posts:
Sagar Shukla
Intern at GeeksforGeeks
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on  the "Improve Article" button below.


Improved By :  jit_t, Mithun Kumar