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math/sum_of_binomial_coefficient.cpp

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+/**
+ * @file
+ * \@brief Program to find sum of binomial coefficients of a given positive integer.
+ * Given a positive integer n, the task is to find the sum of binomial coefficient i.e
+ * nC0 + nC1 + nC2 + ……. + nCn-1 + nCn
+ * By induction, we can prove that the sum is equal to 2^n
+ * [https://en.wikipedia.org/wiki/Binomial_coefficient#Sums_of_the_binomial_coefficients]
+ * @author muskan0719[https://github.com/muskan0719]
+ */
+#include<iostream>
+#include<cassert>
+using namespace std; 
+
+/** 
+ * @param n number
+ * @return Sum of binomial coefficients of number 
+ */
+int binomialCoeffSum(int n) 
+{ 
+    //Calculating 2^n  
+	return (1 << n); 
+}
+/**
+ * Function for testing the binomialCoeffSum() function
+ */ 
+static void test()
+{
+	int test_case_1=binomialCoeffSum(4);
+	assert(test_case_1==16);
+	cout<<"Test_case_1 Passed!"<<endl;
+	int test_case_2=binomialCoeffSum(5);
+	assert(test_case_2==32);
+	cout<<"Test_case_2 Passed!"<<endl;
+ } 
+
+/* Main function*/
+int main() 
+{ 
+    test();
+	int number;
+	cout<<"Enter the value of n"<<endl;
+	cin>>number;
+	assert(number>=0);
+    cout<<"Sum of binomial coefficient is "<<binomialCoeffSum(number)<<endl;
+	return 0; 
+} 
+