Find the sum of series 0.X + 0.XX + 0.XXX +… upto k terms

Given a series of k terms, where ‘X’ is any value between 0-9 and ‘k’ is any positive integer. The task is to find the sum of given series:

0.X + 0.XX + 0.XXX +… up to ‘k’ terms

Examples:



Input: x = 4 , k = 10
Output : 4.39506

Input: x = 9 , k = 20
Output: 19.8889

Explanation:
 $ Result = 0.x + 0.xx + 0.xxx + ...\, up\, to\, k\, terms\\  = x/9(0.9 + 0.99 + 0.999 +... up \, to\, k\, terms)\\  = x/9[(1 - 0.1) + (1 - 0.01) + (1-0.001) + ...\, up\, \, to \, k\, terms]\\  = x/9[(1 + 1 + 1... \, upto\, k \, terms) - (1/10 + 1/100 + 1/1000 + ...\, upto\, k \, terms)]\\  = x/9[n - 0.1 * (1 - (0.1)^k)/(1 - 0.1)]\\  = x/81[9k - 1 + (10)^{-n}]\\ $

C++

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// C++ program for sum of the series
// 0.x,  0.xx, 0.xxx, ... upto k terms
#include <bits/stdc++.h>
using namespace std;
  
// function which return the sum of series
float sumOfSeries(int x, int k)
{
    return (float(x) / 81) * (9 * k - 1 + pow(10, (-1) * k));
}
  
// Driver code
int main()
{
    int x = 9;
    int k = 20;
    cout << sumOfSeries(x, k);
  
    return 0;
}

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Java

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// Java program for sum of the series 
// 0.x,  0.xx, 0.xxx, ... upto k terms 
  
public class GFG {
      
    // function which return the sum of series 
    static float sumOfSeries(int x, int k) 
    
       float y = (float) (((float)(x) / 81) * (9 * k - 1 + Math.pow(10, (-1) * k))); 
       return y ;
    
      
    // Driver code 
    public static void main (String args[]){
         int x = 9
         int k = 20
         System.out.println(sumOfSeries(x, k)); 
    }
  
// This code is contributed by ANKITRAI1
}

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Python3

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#Python3 program for sum of series
#0.x, 0.xx, 0.xxx, ... upto k terms
  
#function which return the sum of series 
def sumOfSeries(x, k):
      
    return (float(x)/81) * (9 * k - 1 + 10**( (-1)*k ) )
      
#Driver code 
if __name__=='__main__':
    x = 9
    k = 20
    print(sumOfSeries(x, k))
# This code is contributed by Shashank Sharma

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C#

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// C# program for sum of the series 
// 0.x, 0.xx, 0.xxx, ... upto k terms 
using System;
  
class GFG 
{
  
// function which return
// the sum of series 
static float sumOfSeries(int x, int k) 
    float y = (float)(((float)(x) / 81) * 
              (9 * k - 1 + Math.Pow(10, (-1) * k))); 
    return y ;
  
// Driver code 
public static void Main ()
{
    int x = 9; 
    int k = 20; 
    Console.Write(sumOfSeries(x, k)); 
}
}
  
// This code is contributed 
// by ChitraNayal

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PHP

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<?php
// PHP program for sum of the series
// 0.x, 0.xx, 0.xxx, ... upto k terms
  
// function which return the
// sum of series
function sumOfSeries($x, $k)
{
    return (($x) / 81) * (9 * $k - 1 +
                      pow(10, (-1) * $k));
}
  
// Driver code
$x = 9;
$k = 20;
echo sumOfSeries($x, $k);
  
// This code is contributed 
// by inder_verma.
?>

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Output:

19.8889


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