递归程序以找到序列的总和1 – 1/2 + 1/3 – 1/4…1 / N

给定正整数N ，任务是找到序列1 –(1/2)+(1/3)–(1/4)+…的和。 (1 / N)使用递归。
例子：

Input: N = 3 
Output: 0.8333333333333333 
Explanation: 
1 – (1/2) + (1/3) = 0.8333333333333333

Input: N = 4 
Output: 0.5833333333333333 
Explanation: 
1- (1/2) + (1/3) – (1/4) = 0.5833333333333333

方法：想法是形成一个递归案例和一个基本案例，以便使用递归解决这个问题。所以：

• 基本情况：此问题的基本情况是当我们计算出总和直到分母中的N值。因此，当计数器变量“ i”达到值N时，我们将停止递归。
• 递归情况：此问题的递归情况是查找分母是偶数还是奇数。这是因为，显然，对于每个奇数，前一个符号是“ +”，对于每个偶数，前一个符号是“-”。因此，我们检查计数器变量是偶数还是奇数，并相应地增加或减少该值。然后，递归地调用该函数以获取值’i’的下一个值。

下面是上述方法的实现：

C++

// C++ program to find the value of 
// the given series
#include
using namespace std;
  
// Recursive program to find the 
// value of the given series
float sumOfSeries(int i, int n, float s) 
{
    // Base case
    if (i > n )
        return s;
   
    // Recursive case
    else 
    {
   
        // If we are currently looking
        // at the even number
        if (i % 2 == 0) 
            s -= (float)1 / i;
   
        // If we are currently looking 
        // at the odd number
        else
            s+= (float)1 / i;
        return sumOfSeries(i + 1, n, s);
    }
}
  
// Driver code
int main()
{
       
    // cout<

---

Java

// Java program to find the value of 
// the given series
import java.util.*;
  
class GFG{
  
// Recursive program to find the 
// value of the given series
static float sumOfSeries(int i, int n, float s) 
{
      
    // Base case
    if (i > n)
        return s;
  
    // Recursive case
    else
    {
          
        // If we are currently looking
        // at the even number
        if (i % 2 == 0) 
            s -= (float)1 / i;
  
        // If we are currently looking 
        // at the odd number
        else
            s += (float)1 / i;
              
        return sumOfSeries(i + 1, n, s);
    }
}
  
// Driver code
public static void main(String[] args)
{
    float sum = sumOfSeries(1, 3, 0);
      
    System.out.printf("%f", sum);
}
}
  
// This code is contributed by Amit Katiyar

Python3

# Python program to find the value of 
# the given series
  
# Recursive program to find the 
# value of the given series
def sumOfSeries(i, n, s) :
  
    # Base case
    if i>n :
        return s
  
    # Recursive case
    else :
  
        # If we are currently looking
        # at the even number
        if i % 2 == 0 :
            s-= 1 / i 
  
        # If we are currently looking 
        # at the odd number
        else :
            s+= 1 / i 
        return sumOfSeries(i + 1, n, s)
  
# Driver code
if __name__ == "__main__":
    print(sumOfSeries(1, 3, 0))

C#

// C# program to find the value of 
// the given series
using System;
class GFG{
  
// Recursive program to find the 
// value of the given series
static float sumOfSeries(int i, int n, float s) 
{
    // Base case
    if (i > n )
        return s;
  
    // Recursive case
    else
    {
  
        // If we are currently looking
        // at the even number
        if (i % 2 == 0) 
            s -= (float)1 / i;
  
        // If we are currently looking 
        // at the odd number
        else
            s += (float)1 / i;
        return sumOfSeries(i + 1, n, s);
    }
}
  
// Driver code
public static void Main()
{
    float sum = sumOfSeries(1, 3, 0);
    Console.Write(sum);
}
}
  
// This code is contributed by Code_Mech

输出：

0.8333333333333333