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}]\\ $](https://neveropen.co.uk/wp-content/uploads/2023/11/rubhabha_quicklatex.com-e9234ad168c721ec9b3c545ad0047ca0_l3.png "Rendered by QuickLaTeX.com")
C++
// C++ program for sum of the series// 0.x, 0.xx, 0.xxx, ... upto k terms#include <bits/stdc++.h>using namespace std;// function which return the sum of seriesfloat sumOfSeries(int x, int k){ return (float(x) / 81) * (9 * k - 1 + pow(10, (-1) * k));}// Driver codeint main(){ int x = 9; int k = 20; cout << sumOfSeries(x, k); return 0;} |
Java
// Java program for sum of the series // 0.x, 0.xx, 0.xxx, ... upto k terms public class GFG { // function which return the sum of series static float sumOfSeries(int x, int k) { float y = (float) (((float)(x) / 81) * (9 * k - 1 + Math.pow(10, (-1) * k))); return y ; } // Driver code public static void main (String args[]){ int x = 9; int k = 20; System.out.println(sumOfSeries(x, k)); }// This code is contributed by ANKITRAI1} |
Python3
#Python3 program for sum of series#0.x, 0.xx, 0.xxx, ... upto k terms#function which return the sum of series def sumOfSeries(x, k): return (float(x)/81) * (9 * k - 1 + 10**( (-1)*k ) ) #Driver code if __name__=='__main__': x = 9 k = 20 print(sumOfSeries(x, k))# This code is contributed by Shashank Sharma |
C#
// C# program for sum of the series // 0.x, 0.xx, 0.xxx, ... upto k terms using System;class GFG {// function which return// the sum of series static float sumOfSeries(int x, int k) { float y = (float)(((float)(x) / 81) * (9 * k - 1 + Math.Pow(10, (-1) * k))); return y ;} // Driver code public static void Main (){ int x = 9; int k = 20; Console.Write(sumOfSeries(x, k)); }}// This code is contributed // by ChitraNayal |
PHP
<?php// PHP program for sum of the series// 0.x, 0.xx, 0.xxx, ... upto k terms// function which return the// sum of seriesfunction sumOfSeries($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.?> |
Javascript
<script>// javascript 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) { var y = (((x) / 81) * (9 * k - 1 + Math.pow(10, (-1) * k))); return y ;} // Driver code var x = 9; var k = 20; document.write(sumOfSeries(x, k)); // This code contributed by shikhasingrajput </script> |
Output:
19.8889
Time Complexity: O(logk), where k is the given integer.
Auxiliary Space: O(1), no extra space is required, so it is a constant.
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