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Sum of the series 0.7, 0.77, 0.777, … upto n terms
  • Difficulty Level : Medium
  • Last Updated : 24 Apr, 2018

Given n the number of terms. Find the sum of the series 0.7, 0.77, 0.777, … upto n terms.

Examples :

Input : 2
Output : 1.46286

Input : 3
Output : 2.23609

Approach Used :
Let’s denote the sum of the series by S:

Sum = 0.7 + 0.77 + 0.777 + …. up to n terms
= 7/9(0.9 + 0.99 + 0.999 + … up to n terms)
= 7/9[(1 – 0.1) + (1 – 0.01) + (1-0.001) + … up to n terms]
= 7/9[(1 + 1 + 1… upto n terms) – (1/10 + 1/100 + 1/1000 + … upto n terms)]
= 7/9[n – 0.1 * (1 – (0.1)n)/(1 – 0.1)]
= 7/81[9n – 1 + 10-n]

Below is the Implementation to find the sum of given series:

C++




// C++ program for sum of the series 0.7, 
// 0.77, 0.777, ... upto n terms
#include <bits/stdc++.h>
using namespace std;
  
// function which return the
// the sum of series
float sumOfSeries(int n)
{
    return .086 * (9 * n - 1 +
           pow(10, (-1) * n));
}
  
// Driver code
int main()
{
    int n = 2;
    cout << sumOfSeries(n);
    return 0;
}


Java




// Java program for sum of the series 0.7, 
// 0.77, 0.777, ... upto n terms
import java.io.*;
import java.math.*;
  
class GFG {
  
    // function which return the
    // the sum of series
    static float sumOfSeries(int n)
    {
        return .086f * (9 * n - 1
        (float)(Math.pow(10, (-1) * n)));
    }
  
    // Driver code
    public static void main(String args[])
    {
        int n = 2;
        System.out.println(sumOfSeries(n));
    }
}
  
/*This code is contributed by Nikita Tiwari.*/


Python3




# Python 3 program for sum of the series 0.7, 
# 0.77, 0.777, ... upto n terms
import math
  
# Function which return the
# the sum of series
def sumOfSeries(n) :
    return .086 * (9 * n - 1 + math.pow(10, (-1) * n));
  
  
# Driver code
n = 2
print(sumOfSeries(n))
  
  
# This code is contributed by Nikita Tiwari.


C#




// C# program for sum of the series  
// 0.7, 0.77, 0.777, ... upto n terms
using System;
  
class GFG {
  
    // Function which return the
    // the sum of series
    static float sumOfSeries(int n)
    {
        return .086f * (9 * n - 1 + 
               (float)(Math.Pow(10, (-1) * n)));
    }
  
    // Driver code
    public static void Main()
    {
        int n = 2;
        Console.Write(sumOfSeries(n));
    }
}
  
// This code is contributed by vt_m.


PHP




<?php
// PHP program for sum of the series 
// 0.7, 0.77, 0.777, ... upto n terms
  
// function which return the
// the sum of series
function sumOfSeries($n)
{
    return .086 * (9 * $n - 1 +
            pow(10, (-1) * $n));
}
  
// Driver code
$n = 2;
echo(sumOfSeries($n));
  
// This code is contributed by Ajit.
?>



Output :

1.46286



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