Approximating the Value of e Using a Unique Expression

How can the value of e be approximated using a specific expression?

The value of e can be approximated using the following expression: (n−1) + n + n / (n−1)

Answer:

To approximate the value of e using the given expression, a program needs to be written.

The program can prompt the user to input a value for 'n' and calculate the approximate value of e accordingly. The expression to be used is (n−1) + n + n / (n−1).

The program should iterate from 0 to 'n' and accumulate the expression for each value of 'i'. The factorial of each 'i' should also be calculated using a separate method.

Finally, the program should print the result with 6 decimal places to provide an accurate approximation of the value of e.

This approach ensures that the value of e can be approximated using a unique expression and provides a practical way to understand its value.