# Sum of all the numbers present at given level in Pascal’s triangle

Given a level L. The task is to find the sum of all the integers present at the given level in Pascal’s triangle .

A Pascal triangle with 6 levels is shown below:

1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

Examples:

Input: L = 3
Output:
1 + 2 + 1 = 4

Input: L = 2
Output:

Approach: If we observe carefully the series of the sum of levels will go on like 1, 2, 4, 8, 16…., which is a GP series with a = 1 and r = 2.
Therefore, sum of Lth level is L’th term in the above series.

`Lth term = 2L-1`

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach`   `#include ` `using` `namespace` `std;`   `// Function to find sum of numbers at ` `// Lth level in Pascals Triangle` `int` `sum(``int` `h)` `{` `    ``return` `pow``(2, h - 1);` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `L = 3;` `    `  `    ``cout << sum(L);` `    `  `    ``return` `0;` `}`

## Java

 `// Java implementation of the approach ` `class` `GFG` `{` `    `  `    ``// Function to find sum of numbers at ` `    ``// Lth level in Pascals Triangle ` `    ``static` `int` `sum(``int` `h) ` `    ``{ ` `        ``return` `(``int``)Math.pow(``2``, h - ``1``); ` `    ``} ` `    `  `    ``// Driver Code ` `    ``public` `static` `void` `main (String[] args)` `    ``{ ` `        ``int` `L = ``3``; ` `        `  `        ``System.out.println(sum(L)); ` `    ``} ` `}`   `// This code is contributed by AnkitRai01`

## Python3

 `# Python3 implementation of the above approach`   `# Function to find sum of numbers at` `# Lth level in Pascals Triangle` `def` `summ(h):` `    ``return` `pow``(``2``, h ``-` `1``)`   `# Driver Code` `L ``=` `3`   `print``(summ(L))`   `# This code is contributed by mohit kumar`

## C#

 `// C# implementation of the approach ` `using` `System;`   `class` `GFG` `{` `    `  `    ``// Function to find sum of numbers at ` `    ``// Lth level in Pascals Triangle ` `    ``static` `int` `sum(``int` `h) ` `    ``{ ` `        ``return` `(``int``)Math.Pow(2, h - 1); ` `    ``} ` `    `  `    ``// Driver Code ` `    ``public` `static` `void` `Main ()` `    ``{ ` `        ``int` `L = 3; ` `        `  `        ``Console.WriteLine(sum(L)); ` `    ``} ` `}`   `// This code is contributed by anuj_67..`

## Javascript

 ``

Output:

`4`

Time Complexity: O(log2L) because it is using pow function
Auxiliary Space: O(1)

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