My professor from Algorithms course gave me the following homework:
Write a C/C++ program that calculates the value of the Euler's number (e) with a given accuracy of eps > 0.
Hint: The number e = 1 + 1/1! +1/2! + ... + 1 / n! + ... = 2.7172 ... can be calculated as the
sum of elements of the sequence x_0, x_1, x_2, ..., where x_0 = 1, x_1 = 1+ 1/1 !, x_2 = 1 + 1/1!
+1/2 !, ..., the summation continues as long as the condition |x_(i+1) - x_i| >= eps is valid.
As he further explained, eps is the precision of the algorithm. For example, the precision could be 1/100
|x_(i + 1) - x_i| = absolute value of ( x_(i+1) - x_i )
Currently, my program looks in the following way:
// Euler's number
using namespace std;
double factorial(double n)
double result = 1;
for(double i = 1; i <= n; i++)
result = result*i;
long double euler = 2;
long double counter = 2;
float epsilon = 2;
euler+= pow(factorial(counter), -1);
while( (euler+1) - euler >= epsilon);
cout << euler << endl;
The problem comes when I implement the stop condition |x_(i+1) - x_i| > = eps (line where is while( (euler+1) - euler >= epsilon);)
The output is 2.5 instead of 2.71828