Skip to content
Related Articles

Related Articles

Improve Article
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)
 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer Geeks Classes Live




My Personal Notes arrow_drop_up
Recommended Articles
Page :