In mathematics, there are many series whose sum is calculated using computer programs to reduces the effort of doing enormous computations. This example program computes the sum of series ( ). The user has to input the value of n.

To write such programs you must be careful about two things – accuracy and type conversions. Accuracy means correct to at least 3 decimal places because series involves real values. A small difference can produce wrong results.

Sometimes we need to do arithmetic between an integer value and a float value. In such cases, to get the correct value of the expression to convert both operands into the same type using C++ type cast operator.

Before you begin, learn basics of C++ programming. Continue reading if you are familiar with the basics.

- C++ program structure
- How to install Turbo C++ compiler
- How to compile a program using Turbo C++ compiler
- C++ data type classification

## Problem Definition

We want to write a program that computes the sum of the following series and prints an output to the console.

n^2/(n-1)

When the program runs, the user provides the value of and the program computes the sum of all values up to n. The program cannot have a value less than because any value less than is *undefined*.

For example,

\begin{aligned} &if \hspace{5px} n = 1\\\\ &= 1^2/(1 - 1)\\\\ &= 1/0\\\\ &= Undefined \end{aligned}

To understand the problem let us do a manual computation and verify the results using our example program. Suppose , then

\begin{aligned} &= \frac{2^2}{(2 - 1)} + \frac{3^2}{(3-1)} + \frac{4^2}{(4-1)}+\frac{ 5^2}{(5-1)}\\\\ &= 4/1 + 9/2 + 16/3 + 25/4\\\\ &= 20.08 \end{aligned}

You can use a calculator or do fraction addition. The final sum of the series is given below.

Now, you need to verify the output by running the C++ program for the sum of the series given below.

## Program Source Code

```
#include <cstdlib>
#include <iostream>
using namespace std;
int main(){
int n,i;
double sum;
//initialize sum to 0
sum = 0.0;
//read value of N
cout << "Enter the value of n:";
cin >> n;
//Compute the value of the sum, but the equation has a restriction.
//The value of n should not be less than 2
for(i=2;i<=n;i++)
{
sum = sum + float(i * i)/float(i-1);
}
//Printing the Output to Console
cout << "\n";
cout << "Sum of the Series n^2/(n-1) =" << " " << sum << endl;
cout << "\n";
system("PAUSE");
return EXIT_SUCCESS;
}
```

## Output

The output of the program is the same what we received using manual computation method. Therefore, the program works correctly. You may try different inputs.

```
Enter the value of n:5
Sum of the Series n^2/(n-1) = 20.0833
Press any key to continue . . .
```