Assignment Example: Cyclic Functions

Task

\sum_{x=1}^{5} \sum_{k=0}^{\infty} \frac{(-1)^k x^{2k-1}}{(k+x)!k!}

Block scheme of the solution:

sample-cyclic-functions-1

С++ implementation:


#include<iostream> 
#include<math.h> 
#include<iomanip>
using namespace std;
float error;
float factorial(int n)
{
float factorial = 1;
for (n; n>0; n--)
factorial *= n;
return factorial;
}
float sum = 0, item;
void main()
{
cout << "(-1^k*x^(2k-1))/(!(k+x)*!k)" << endl;
cout << "Input the error:"; cin >> error;


for (int x = 1; x <= 5; x++)
{
for (int k = 0; k <= 18; k++)//k - float overflowing border 
{
item = (pow(-1, k)*pow(x, 2 * k - 1)) / (factorial(k + x)*factorial(k));//calculate item 
if (error <= fabs(item))
{
sum += item;//summing items 
cout << setw(5) << x << setw(5) << k << setw(25) << item << setw(25) << sum << endl;//intervals & output 
}
}
cout << "______________________________________________________________overflow" << endl;
}
cout << endl << "sum=" << sum << endl;//output sum 
system("pause");//pause console 
}

Screenshot of the working program:

sample-cyclic-functions-2

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