computing for the value of e

[masquechique]

Hoi!
I'm supposed to get the value of e by summing 1 and the inverse of factorials from 1 to 5 (i.e. e = 1 + 1/1! + 1/2!+...+1/5!). I edited the code and now I get "The value of e is approximately 134513785."

#include<stdio.h>
int main(void)
{
int e, x, y;
double factorial;
for (x=5; x>=1; x--)
{
for (y=5; y>=1; y--)
{
factorial *= y;
}
x = 1/factorial;
}
e += 1 + x;
printf("The value of e is approximately %d.\n", e);
return 0;
}

and then with the following code i get "The value of e is approximately equal to 0."
#include<stdio.h>
int main(void)
{
int e, x, y;
double factorial;
for (x=5; x>=1; x--)
{
for (y=5; y>=1; y--)
{
factorial *= y;
}
x = 1/factorial;
}
e = 1 + x;
printf("The value of e is approximately %d.\n", e);
return 0;
}

[smilodon]

get the value of e

You are not finding e; you are approximating e.

#include<stdio.h>
int main(void)
{
  int e, x, y;
  double factorial;
  for (x=5; x>=1; x--)
  {
     for (y=5; y>=1; y--)
     {
         factorial *= y;
     }
     x = 1/factorial;
  }
  e = 1 + x;
  printf("The value of e is approximately %d.\n", e);
  return 0;
} 

after slightly reformatting you code, I cannot understand how the x loop will run more than once

[masquechique]

yes, sorry

i keep getting the value 1

[smilodon]

after slightly reformatting you code, I cannot understand how the x loop will run more than once

[masquechique]

i think i said incorrectly, i don't mean that the x loop will run more than once, but because i get such a large value (134513785), i thought that it was because when the next value for x is computed, the factorial of the previous value of x adds to the factorial of the next value.

[smilodon]

With c++ when you initialize a variable it is almost always set to zero. What probably happened is that you did 1/0 and the program just did something with it, also 1/factorial will most likely be a float less than 1.

[masquechique]

my friend said something about putting an if else statement after the 2nd for loop but i don't get how it was done. how do you guys think it was done?

[johnkravetzki]

you are very close to find the solution, just follow carefully @smilodon's hints. Focus on your factorial - let's say you have to count 5! which is 1*2*3*4*5. How to implement it now?

double factorial = 1;
for(int i = 1; i <= 5; i++) 
    factorial *= i; 

Now compare it with your code - notice, you're computing the factorial using an extra loop, which gives you a false result (n! powered by n if I count correctly)

any conclusion? i guess you already have done it...

Another hint is concerning the Euler's number (e). According to the formula, e=

----
\
/ 1/n! where n€<0,+inf) or just 1+ 1/n! (n€<1,+inf) since 0! = 1)
----

in that case we can assign value of "1" to our e number, here we go:

#include <iostream>
#include <iomanip> 
using namespace std;
int main()
{
     double factorial = 1;
     double e = 1;     //we will add only 1/n!, since 1 is already assigned
    
     for(int i = 1; i <= N; i++)  //change N to any number, greater N == better approximation
     {
          factorial *= i;  //computing the factorial
          e += 1/factorial;   // 1 is already assigned
     }
     
     cout<<setprecision(14)<<e;   // for s.p.(14)  e = 2,718281828459
     
     return 0;
}

[masquechique]

Alright! Thank you very much.
now i get the looping problem, thanks!