# Sum of the sequence 2, 22, 222, ………

Last Updated : 25 Jan, 2023

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 ` `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

 ``

## Javascript

 ``

Output

`245.986`

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

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