How Can I Write this Formula in C#? (What is wrong with The way I code ?)

Question

Hope your ok I'll be happy if you help me out with this problem ... Thnx

I wrote this Code for the Formula : "http://up.upinja.com/zvhev.png"

Console.WriteLine("Enter two Numbers to start the Equation (X=Number , N=Power)" + "");
int X = int.Parse(Console.ReadLine());
int N = int.Parse(Console.ReadLine());
double sum = 0;
double up = 1;
int down = 1;

double sentence;
for (int i = 1; i < N; i++)
{
up = Math.Pow(X, N);
down = N * i;
sentence = up / down;
sum += sentence;
}
Console.WriteLine("The Sum is : " + sum);

---

I want that math Formula to be done in C# way.... my Code is running but wrong answer I get ... Could you plz help me to fix it ?

Answer 1

n! represents Factorial. Please refer Factorial to read about Factorial.

A sample factorial function in C# is as follows:

long Factorial(long value)
{          
    if (value == 0)
        return 1;

    return value * Factorial(value - 1);
}

Also, following line needs correction.

up = Math.Pow(X, N);

The exponent part needs to increase according to your formula. It needs to be

up = Math.Pow(X, i);

Answer 2

Use this:

Console.WriteLine("Enter two Numbers to start the Equation (X=Number , N=Power)" + "");
int X = int.Parse(Console.ReadLine());
int N = int.Parse(Console.ReadLine());
double sum = 0;
double up = 1;
int down = 1;

double sentence;
for (int i = 1; i <= N; i++)
//Change < to <=
{
    up = Math.Pow(X, i);
    //This is a for loop i created to get the factorial of any number, sometimes creating your own functions may be worth it
    for (int a = N, a > 0, a--)
    {
     //Function of this Loop : multiply the value of the denominator by its value - 1 to get the factorial of  the number
        down *= a;
    } 
    sentence = up / down;
    sum += sentence;
}
Console.WriteLine("The Sum is : " + sum);

Answer 3

You can actually simplify this quite a bit. But first, what's wrong with your existing code is that you're not computing i! correctly. The sequence you're actually computing right now is:

X^N / N + X^N / (2 * N) + X^N / (3 * N) + ... + X^N / ((N - 1) * N)

A few things: - The loop has an off-by-one issue - The numerator is raised to the wrong power - The denominator of these needs to be i!

Factorials are defined through a simple recurrence relation:

i! = i * (i - 1)! and 0! = 1

Or, in other words, the product of the first i consecutive natural numbers. So one way to correct this is by creating a method called Factorial:

static long Factorial(int i) 
{ 
    long product = 1;
    while (i > 0) {
        product *= i;
        --i;
    }
    return product;
}

Then you can fix your loop this way:

for (int i = 1; i < N; i++)
{
    sum += Math.Pow(X, i) / Factorial(i);
}

However, we're redoing a lot of work every iteration of the loop that we don't need to do. This is where the simplification comes in. The general formula for the i'th term is this:

C[i] = X^i / i!

But we can also write this in terms of the term that came before it:

C[i] = C[i-1] * X / i

So we can rewrite the loop like this:

double lastTerm = 1;
for (int i = 1; i <= N; ++i)
{
    // Cast to double here or, probably better, make X a double in the first place.
    lastTerm *= (double) X / i;
    sum += lastTerm;
}

This has several advantages:

• It'll generally be faster since we're doing less work each iteration (Math.Pow computes arbitrary powers, so it's a bit slower than just multiplying).
• It'll be less prone to numerical issues. Factorials get really big really fast. In fact, 21! is already too big to store in a long so if your N is bigger than that, everything will break.

Answer 4

Something wrong in pow, shoud incremental value

    up = Math.Pow(X, i);