Calculate sum of n number of terms in Maclaurin's series and graphically show that error in calculation decreases with the increasing number of terms

keith.cpp

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+// C++ program to check if a number is Keith or not 
+
+#include<bits/stdc++.h> 
+using namespace std; 
+
+// Returns true if x is Keith, else false. 
+bool isKeith(int x) 
+{ 
+	// Store all digits of x in a vector "terms" 
+	// Also find number of digits and store in "n". 
+	vector <int> terms; 
+	int temp = x, n = 0; // n is number of digits in x 
+	while (temp > 0) 
+	{ 
+		terms.push_back(temp%10); 
+		temp = temp/10; 
+		n++; 
+	} 
+
+	// To get digits in right order (from MSB to 
+	// LSB) 
+	reverse(terms.begin(), terms.end()); 
+
+	// Keep finding next trms of a sequence generated 
+	// using digits of x until we either reach x or a 
+	// number greate than x 
+	int next_term = 0, i = n; 
+	while (next_term < x) 
+	{ 
+		next_term = 0; 
+
+		// Next term is sum of previous n terms 
+		for (int j=1; j<=n; j++) 
+			next_term += terms[i-j]; 
+
+		terms.push_back(next_term); 
+		i++; 
+	} 
+
+	/* When the control comes out of the while loop, 
+	either the next_term is equal to the number 
+	or greater than it. 
+	If next_term is equal to x, then x is a 
+	Keith number, else not */
+	return (next_term == x); 
+} 
+
+// Driver program 
+int main() 
+{ 
+isKeith(14)? cout << "Yes\n" : cout << "No\n"; 
+isKeith(12)? cout << "Yes\n" : cout << "No\n"; 
+isKeith(197)? cout << "Yes\n" : cout << "No\n"; 
+return 0; 
+} 

lucas.cpp

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+// Iterative C/C++ program 
+// to find n'th Lucas Number 
+#include <stdio.h> 
+
+// Iterative function 
+int lucas(int n) 
+{ 
+	// declaring base values 
+	// for positions 0 and 1 
+	int a = 2, b = 1, c, i; 
+
+	if (n == 0) 
+		return a; 
+
+	// generating number 
+	for (i = 2; i <= n; i++) 
+	{ 
+		c = a + b; 
+		a = b; 
+		b = c; 
+	} 
+	return b; 
+} 
+
+// Driver Code 
+int main() 
+{ 
+	int n = 9; 
+	printf("%d", lucas(n)); 
+	return 0; 
+} 

pell number.cpp

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+// Iterative Pell Number Series in C 
+#include <stdio.h> 
+
+// calculate nth pell number 
+int pell(int n) 
+{ 
+	if (n <= 2) 
+		return n; 
+
+	int a = 1; 
+	int b = 2; 
+	int c, i; 
+	for (i = 3; i <= n; i++) { 
+		c = 2 * b + a; 
+		a = b; 
+		b = c; 
+	} 
+	return b; 
+} 
+
+// driver function 
+int main() 
+{ 
+	int n = 4; 
+	printf("%d", pell(n)); 
+	return 0; 
+} 

pronic number.cpp

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+// C/C++ program to check if a number is pronic or not 
+
+#include<bits/stdc++.h> 
+using namespace std; 
+
+// function to check Pronic Number 
+bool pronic_check(int n) 
+{ 
+	int x = (int)(sqrt(n)); 
+
+	// Checking Pronic Number by 
+	// multiplying consecutive numbers 
+	if (x*(x+1)==n) 
+		return true; 
+	else
+		return false; 
+} 
+
+// Driver Code 
+int main(void) 
+{ 
+	int n = 56;	 
+	pronic_check(n) == true? cout << "YES" : 
+							cout << "NO"; 
+
+	return 0; 
+}