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 = 2print(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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