Threaded Mode | Linear Mode

***drdebcol*** · (This post was last modified: 12-04-2009 04:32 AM by drdebcol.)

Base of natural algorithm "e" is a number that you can not write in p/q way so it is irrational. You need to make like an array of numbers with certain rule so you can get it with accuracy. "e" is around :

Code:

2.71828 18284 59045 23536 . . .

More about natural logarithm you have here :
http://en.wikipedia.org/wiki/Natural_logarithm
And about "e" you have here :
http://en.wikipedia.org/wiki/E_%28mathem...onstant%29
Now you can calculate exponent of "e" with this formula :
[Image: 22783_exponente.jpg]

And i made program for calculating this in Pascal. Input data are "n" and "x". "n" is number of loop circulations and "x" is exponent.
If you enter :
n=20
x=1
you should get around :
2.7182818
So here is the code in TPW for this :

Code:

program natural_logarithm_exponent;

uses wincrt;

var

i,n:longint;

e,x,p:real;

function power(a:real;b:longint):real;

var

  i:longint;

  p:real;

begin

  p:=1;

  for i:=1 to b do

    p:=p*a;

  power:=a;

end;

begin

readln(n);

readln(x);

p:=1;

e:=0;

for i:=1 to n do

 begin

  e:=e+power(x,i)/p;

  p:=p*i;

 end;

 writeln(e:9:7);

end.

And now solution in C++. Basically you didn't have to make power function in Pascal. As you can see, C++ solution is much
more simple and evidently faster :

Code:

# include <iostream>

# include <cstdio>

using namespace std;

int main()

{

    int i,n;

    float e,x,p;

    cin>>n;

    cin>>x;

    p=1;

    e=0;

    for (i=1;i<=n;i++)

    { 

        e+=(x/p);

        x=x*x; 

        p*=i;

    }

    cout<<e<<endl;

    system("pause");

}