Sum of the sequence 2, 22, 222, ………

Find the sum of the following sequence : 2, 22, 222, ……… to n terms. 
Examples :

Input : 2
Output: 23.99868

Input : 3
Output: 245.98647

A simple solution is to compute terms one by one and add to the result.
The above problem can be efficiently solved using the following formula:

C++14

// CPP program to find sum of series
// 2, 22, 222, ..
#include <bits/stdc++.h>
using namespace std;

// function which return the
// the sum of series
float sumOfSeries(int n)
{
    return 0.02469 * (10*(pow(10, n) - 1)- (9 * n));
}

// driver code
int main()
{
    int n = 3;
    cout << sumOfSeries(n);
    return 0;
}

Java

// JAVA Code for Sum of the
// sequence 2, 22, 222,...
import java.util.*;

class GFG {

    // function which return the
    // the sum of series
    static double sumOfSeries(int n)
    {
        return 0.02469 * ((10*Math.pow(10, n)
                            - 1) - (9 * n));
    }

    /* Driver program */
    public static void main(String[] args)
    {
         int n = 3;
         System.out.println(sumOfSeries(n));
    }
}

// This code is contributed by Arnav Kr. Mandal.

Python3

# Python3 code to find
# sum of series
# 2, 22, 222, ..
import math

# function which return
# the sum of series
def sumOfSeries( n ):
    return 0.02469 * ((10*math.pow(10, n) - 1 )- (9 * n))

# driver code
n = 3
print( sumOfSeries(n))

# This code is contributed by "Sharad_Bhardwaj".

C#

// C# Code for Sum of the
// sequence 2, 22, 222,...
using System;

class GFG {

    // Function which return the
    // the sum of series
    static double sumOfSeries(int n)
    {
        return 0.02469 * ((10*Math.Pow(10, n)
                           - 1) - (9 * n));
    }

    // Driver Code
    public static void Main()
    {
        int n = 3;
        Console.Write(sumOfSeries(n));
    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP program to find sum
// of series 2, 22, 222, ..

// function which return the
// the sum of series
function sumOfSeries($n)
{
    return 0.02469 * ((10*pow(10, $n) -
                     1 )- (9 * $n));
}

// Driver Code
$n = 3;
echo(sumOfSeries($n));

// This code is contributed by Ajit.
?>

Javascript

<script>

// JavaScript program for Sum of the
// sequence 2, 22, 222,...

    // function which return the
    // the sum of series
    function sumOfSeries(n)
    {
        return 0.0246 * ((10*Math.pow(10, n)
                            - 1) - (9 * n));
    }

// Driver code

        let n = 3;
        document.write(sumOfSeries(n));

</script>

Output

245.986

Time complexity: O(log n) since using inbuilt power function.
Auxiliary Space: O(1)