Sum of the series 0.7, 0.77, 0.777, … upto n terms

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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 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 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 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 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 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. 
?> 

Javascript

<script> 
  
// javascript program for sum of the series 0.7,  
// 0.77, 0.777, ... upto n terms 
  
// function which return  
// the sum of series 
function sumOfSeries( n) 
{ 
    return .086 * (9 * n - 1 + 
           Math.pow(10, (-1) * n)); 
} 
// Driver Code 
let n = 2 ; 
   document.write(sumOfSeries(n).toFixed(5)) ;  
     
// This code contributed by aashish1995 
  
</script> 

Output:

1.46286

Time Complexity: O(logn), where n is the given integer.

Auxiliary Space: O(1), no extra space is required, so it is a constant.

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