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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 <bits/stdc++.h>
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




<script>
 
// Javascript implementation of the above approach
 
// Function to find sum of numbers at
// Lth level in Pascals Triangle
function sum(h)
{
    return Math.pow(2, h - 1);
}
 
// Driver Code
var L = 3;
 
document.write(sum(L));
 
</script>
Output: 
4

 

Time Complexity: O(1)
 

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