Given a positive integer n, the task is to find the sum of series
8/10 + 8/100 + 8/1000 + 8/10000. . . till Nth term
Examples:
Input: n = 3
Output: 0.888Input: n = 5
Output: 0.88888
Approach:
The total sum till nth term of the given G.P. series can be generalized as-
The above formula can be derived following the series of steps-
The given G.P. series
Here,
Thus, using the sum of G.P. formula for r<1
Substituting the values of a and r in the above equation
Illustration:
Input: n = 3
Output: 0.888
Explanation:
S_{n}=\frac{8}{9}(1-(\frac{1}{10})^{3})
= 0.888 * 0.999
= 0.888
Below is the implementation of the above problem-
// C++ program to implement // the above approach #include <bits/stdc++.h> using namespace std;
// Function to calculate sum of // given series till Nth term double sumOfSeries( double N)
{ return (8 * (( pow (10, N) - 1) / pow (10, N))) / 9;
} // Driver code int main()
{ double N = 5;
cout << sumOfSeries(N);
return 0;
} |
// Java program to implement // the above approach import java.util.*;
public class GFG
{ // Function to calculate sum of
// given series till Nth term
static double sumOfSeries( double N)
{
return ( 8
* ((Math.pow( 10 , N) - 1 ) / Math.pow( 10 , N)))
/ 9 ;
}
// Driver code
public static void main(String args[])
{
double N = 5 ;
System.out.print(sumOfSeries(N));
}
} // This code is contributed by Samim Hossain Mondal. |
# Python code for the above approach # Function to calculate sum of # given series till Nth term def sumOfSeries(N):
return ( 8 * ((( 10 * * N) - 1 ) / ( 10 * * N))) / 9 ;
# Driver code N = 5 ;
print (sumOfSeries(N));
# This code is contributed by gfgking |
// C# program to implement // the above approach using System;
class GFG
{ // Function to calculate sum of
// given series till Nth term
static double sumOfSeries( double N)
{
return (8
* ((Math.Pow(10, N) - 1) / Math.Pow(10, N)))
/ 9;
}
// Driver code
public static void Main()
{
double N = 5;
Console.WriteLine(sumOfSeries(N));
}
} // This code is contributed by ukasp. |
<script> // JavaScript code for the above approach
// Function to calculate sum of
// given series till Nth term
function sumOfSeries(N) {
return (8 * ((Math.pow(10, N) - 1) / Math.pow(10, N))) / 9;
}
// Driver code
let N = 5;
document.write(sumOfSeries(N));
// This code is contributed by Potta Lokesh
</script>
|
Output
0.88888
Time Complexity: O(log n)
Auxiliary Space: O(1)