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.