Find the Sum of the series 1/2 – 2/3 + 3/4 – 4/5 + … till N terms
Given a number N, the task is to find the sum of the below series till N terms.
Examples:
Input: N = 6
Output: -0.240476
Input: N = 10
Output: -0.263456
Approach: From the given series, find the formula for Nth term:
1st term = 1/2 2nd term = - 2/3 3rd term = 3/4 4th term = - 4/5 . . Nthe term = ((-1)N) * (N / (N + 1))
Therefore:
Nth term of the series
*** QuickLaTeX cannot compile formula: *** Error message: Error: Nothing to show, formula is empty
Then iterate over numbers in the range [1, N] to find all the terms using the above formula and compute their sum.
Below is the implementation of the above approach:
C++
// C++ program for the above approach #include <bits/stdc++.h> using namespace std; // Function to find the sum of series void printSeriesSum( int N) { double sum = 0; for ( int i = 1; i <= N; i++) { // Generate the ith term and // add it to the sum if i is // even and subtract if i is // odd if (i & 1) { sum += ( double )i / (i + 1); } else { sum -= ( double )i / (i + 1); } } // Print the sum cout << sum << endl; } // Driver Code int main() { int N = 10; printSeriesSum(N); return 0; } |
Java
// Java program for the above approach class GFG{ // Function to find the sum of series static void printSeriesSum( int N) { double sum = 0 ; for ( int i = 1 ; i <= N; i++) { // Generate the ith term and // add it to the sum if i is // even and subtract if i is // odd if (i % 2 == 1 ) { sum += ( double )i / (i + 1 ); } else { sum -= ( double )i / (i + 1 ); } } // Print the sum System.out.print(sum + "\n" ); } // Driver Code public static void main(String[] args) { int N = 10 ; printSeriesSum(N); } } // This code is contributed by 29AjayKumar |
Python3
# Python3 program for the above approach # Function to find the sum of series def printSeriesSum(N) : sum = 0 ; for i in range ( 1 , N + 1 ) : # Generate the ith term and # add it to the sum if i is # even and subtract if i is # odd if (i & 1 ) : sum + = i / (i + 1 ); else : sum - = i / (i + 1 ); # Print the sum print ( sum ); # Driver Code if __name__ = = "__main__" : N = 10 ; printSeriesSum(N); # This code is contributed by Yash_R |
C#
// C# program for the above approach using System; class GFG { // Function to find the sum of series static void printSeriesSum( int N) { double sum = 0; for ( int i = 1; i <= N; i++) { // Generate the ith term and // add it to the sum if i is // even and subtract if i is // odd if ((i & 1)==0) { sum += ( double )i / (i + 1); } else { sum -= ( double )i / (i + 1); } } // Print the sum Console.WriteLine(sum); } // Driver Code public static void Main ( string [] args) { int N = 10; printSeriesSum(N); } } // This code is contributed by shivanisinghss2110 |
Javascript
<script> // javascript program for the above approach // Function to find the sum of series function printSeriesSum( N) { let sum = 0; for (let i = 1; i <= N; i++) { // Generate the ith term and // add it to the sum if i is // even and subtract if i is // odd if (i & 1) { sum += i / (i + 1); } else { sum -= i / (i + 1); } } // Print the sum document.write( sum.toFixed(6) ); } // Driver Code let N = 10; printSeriesSum(N); // This code is contributed by todaysgaurav </script> |
Output:
-0.263456
Time complexity: O(n) for given input n
Auxiliary Space: O(1), since no extra space has been taken.