Sum of the series 5+55+555+.. up to n terms
Find the sum up to n terms of the sequence: 5 + 55 + 555 + … up to n.
Examples :
Input : 2 Output: 60 Input : 3 Output: 595
Approach:The above problem can be solved using the following formula:
Sum = 5 + 55 + 555 + …. n terms.
= 5/9[9 + 99 + 999 + …. n terms]
= 5/9[(10 – 1) + (100 – 1) + (1000 – 1) + … n terms]
= 5/9[10 + 100 + 1000 ….. – (1 + 1 + … 1)]
= 5/9[10(10n – 1)/(10 – 1) + (1 + 1 + … n times))
= 50/81(10n – 1) – 5n/9
Below is the Implementation to find the sum of given series:
C++
// C++ program for sum of the // series 5 + 55 + 555.....n #include <bits/stdc++.h> using namespace std; // function which return the // the sum of series int sumOfSeries(int n) { return 0.6172 * (pow(10, n) - 1) - 0.55 * n; } // Driver code int main() { int n = 2; cout << sumOfSeries(n); return 0; } |
Java
// Java program for sum of the // series 5 + 55 + 555.....n class GFG { // function which return the // the sum of series static int sumOfSeries(int n) { return (int) (0.6172 * (Math.pow(10, n) - 1) - 0.55 * n); } // Driver code public static void main(String []args) { int n = 2; System.out.println(sumOfSeries(n)); } } // This code is contributed by UPENDRA BARTWAL. |
Python3
# python program for sum of the # series 5 + 55 + 555.....n def sumOfSeries(n): return (int) (0.6172 * (pow(10, n) - 1) - 0.55 * n) # Driver Code n = 2print(sumOfSeries(n)) # This code is contributed # by Upendra Singh Bartwal |
C#
// C# program for sum of the // series 5 + 55 + 555.....n using System; class GFG { // Function which return the // the sum of series static int sumOfSeries(int n) { return (int)(0.6172 * (Math.Pow(10, n) - 1) - 0.55 * 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 5 + 55 + 555.....n // function which return the // the sum of series function sumOfSeries($n) { return (int)(0.6172 * (pow(10, $n) - 1) - 0.55 * $n); } // Driver code $n = 2; echo(sumOfSeries($n)); // This code is contributed by Ajit. ?> |
Output :
60
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