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 = 2
print (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. ?> |
Javascript
<script> // javascript program for sum of the // series 5 + 55 + 555.....n // function which return the
// the sum of series
function sumOfSeries(n) {
return parseInt( (0.6172 * (Math.pow(10, n) - 1) - 0.55 * n));
}
// Driver code
var n = 2;
document.write(sumOfSeries(n));
// This code is contributed by aashish1995 </script> |
Output :
60
Time complexity: O(log n) since using the inbuilt power function.
Auxiliary Space: O(1)