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Find Range Value of the Expression

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  • Last Updated : 10 Mar, 2022
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Given two integers L and R, the task is to calculate the value of the expression: 

    $$F = \sum_{i=L}^{R} \frac{1}{i^2 + i} $$

Examples: 
 

Input: L = 6, R = 12 
Output: 0.09
Input: L = 5, R = 6 
Output: 0.06 
 

 

Approach: It can be observed that \frac{1}{i^2 + i} = \frac{1}{i} - \frac{1}{i + 1}   .
So, F = \sum_{i=L}^{R} \frac{1}{i^2 + i} = (\frac{1}{L} - \frac{1}{L + 1}) + (\frac{1}{L + 1} - \frac{1}{L + 2}) + .... + (\frac{1}{R} - \frac{1}{R + 1}) = (\frac{1}{L} - \frac{1}{R + 1})
Hence, the answer will be (1 / L) – (1 / (R + 1)).
Below is the implementation of the above approach: 
 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the value
// of the given expression
double get(double L, double R)
{
 
    // Value of the first term
    double x = 1.0 / L;
 
    // Value of the last term
    double y = 1.0 / (R + 1.0);
 
    return (x - y);
}
 
// Driver code
int main()
{
    int L = 6, R = 12;
 
    // Get the result
    double ans = get(L, R);
    cout << fixed << setprecision(2) << ans;
 
    return 0;
}

Java




// Java implementation of the approach
import java.util.*;
 
class GFG
{
 
// Function to return the value
// of the given expression
static double get(double L, double R)
{
 
    // Value of the first term
    double x = 1.0 / L;
 
    // Value of the last term
    double y = 1.0 / (R + 1.0);
 
    return (x - y);
}
 
// Driver code
public static void main(String []args)
{
    int L = 6, R = 12;
 
    // Get the result
    double ans = get(L, R);
    System.out.printf( "%.2f", ans);
}
}
 
// This code is contributed by Surendra_Gangwar

Python3




# Python3 implementation of the approach
 
# Function to return the value
# of the given expression
def get(L, R) :
 
    # Value of the first term
    x = 1.0 / L;
 
    # Value of the last term
    y = 1.0 / (R + 1.0);
 
    return (x - y);
 
# Driver code
if __name__ == "__main__" :
 
    L = 6; R = 12;
 
    # Get the result
    ans = get(L, R);
    print(round(ans, 2));
 
# This code is contributed by AnkitRai01

C#




     
// C# implementation of the approach
using System;
 
public class GFG
{
  
// Function to return the value
// of the given expression
static double get(double L, double R)
{
  
    // Value of the first term
    double x = 1.0 / L;
  
    // Value of the last term
    double y = 1.0 / (R + 1.0);
  
    return (x - y);
}
  
// Driver code
public static void Main(String []args)
{
    int L = 6, R = 12;
  
    // Get the result
    double ans = get(L, R);
    Console.Write( "{0:F2}", ans);
}
}
 
// This code contributed by PrinciRaj1992

Javascript




<script>
// JavaScript implementation of the approach
 
// Function to return the value
// of the given expression
function get(L, R)
{
 
    // Value of the first term
    let x = 1.0 / L;
 
    // Value of the last term
    let y = 1.0 / (R + 1.0);
    return (x - y);
}
 
// Driver code
    let L = 6, R = 12;
 
    // Get the result
    let ans = get(L, R);
    document.write(Math.round(ans * 100) / 100);
 
// This code is contributed by Surbhi Tyagi.
</script>

Output: 

0.09

 

Time Complexity: O(1)

Auxiliary Space: O(1)
 


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