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Sum of all the numbers present at given level in Pascal’s triangle
• Last Updated : 01 Apr, 2021

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 as 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(1)

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