Styjun

example of code

#include <iostream>
using namespace std;
//whitespace package
#include <iomanip>
#include <math.h>
using std::setw;

int main () 

 // n is an array of 101 integers
 double n[ 101 ];
 double exponent=3;
 double fraction=1/7;

 // initialize elements of array n to 0
 for ( int i = 1; i < 100; i++ ) 
 n[ i ] = 0;
 

 //what is input 1?
 cout << "Enter x_1" << endl;
 cin >> n[1];

 //jam ni's into function and loop
 for ( int i = 1; i < 100; i++ ) 

 // set element at location i+1 to f(x)= (fraction)*((x)^exponent + 2)
 n[ i + 1 ] = fraction*(pow( ((n[ i ]) ), exponent ) + 2);
 

 //header
 cout << "Element" << setw( 13 ) << "Value" << endl;

 // output each array element's value
 for ( int j = 1; j < 100; j++ ) 
 cout << setw( 7 )<< j << setw( 13 ) << n[ j ] << endl;
 

 return 0;

output

Enter x_1
1
Element Value
 1 1
 2 0
 3 0
 4 0
 5 0
 6 0
 7 0
 8 0
 9 0
 10 0

....

where my expected output would be

Element Value
 1 1
 2 0.42857142857
 3 0.29695960016
 4 0.2894553405
 5 0.28917883433
 6 0.28916891514
 7 0.28916855966

...

background: I'm trying to write a simple program that asks what your $x_1$ is and reports $x_1$ to $x_100$ given some series function calculator--like a sequence calculator where $x_n+1 = f(x_n)$. In this example, our function is (1/7)*((x)^3 + 2).

Can you all offer some resources for writing other functions? I have $x_n+1=f(x_n)=(1/7)*((x_n^3)+2)$ right now.

Whenever I look up c++ math functions I get things like how to use the absolute value function, or how to use my cpp file as a function itself, but not information on writing math functions like this.

To report x_1 to x_100 you don't need an array of 101 elements but an array of 100 elements, indexed from 0 inclusive to 100 exclusive. The index of the array is one less than the order of the element of the sequence starting at order 1.

You can use value initialization to set all the elements of the array to 0 in same statement than the declaration.

In C++ the result of division of two integers is an integer, this why your fraction number was 0. So to obtain a non-truncated value, one of the operands should be double (the other will be promoted to double by the compiler before the division).

#include <cmath>
#include <iomanip>
#include <iostream>

using namespace std;

constexpr size_t elems_len = 100;

int main()

 double n[elems_len]; // value initialization, all elements of n are set to 0 
 double exponent = 3;

 // one of the operands should be double to avoid integer division and truncation 
 double fraction = 1.0 / 7;

 cout << "Enter x_1" << endl;
 cin >> n[0];

 for (size_t i = 1; i < elems_len; i++) 
 n[i] = fraction * (pow(n[i-1], exponent) + 2);
 

 cout << "Element" << setw(13) << "Value" << endl;

 cout << fixed << setprecision(11);
 for (size_t i = 0; i < elems_len; i++) 
 cout << setw(7) << i + 1 << setw(25) << n[i] << endl;