Find Nth term of the series 1^3/1+(1^3+2^3)/(1+3)+(1^3+2^3+3^3)/(1+3+5)+…
Given a positive integer N. The task is to find Nth term of the series:
Examples:
Input: N = 2
Output: 2.25Input: N = 3
Output: 4
Approach:
From the given series, find the formula for Nth term:
1st term = 1^3/1 = 1/1 = 1
2nd term = (1^3+2^3)/(1+3) = (1+8)/4 = 9/4 = 2.25
3rd term = (1^3+2^3+3^3)/(1+3+5) = (1+8+27)/9 = 4
4th term = (1^3+2^3+3^3+4^3)/(1+3+5+7) = (1+8+27+64)/16 = 6.25
.
.
Nth term = ((N*(N+1)/2)^2)/(N*(2+(N-1)*2)/2) = (N+1)^2/4 = (N^2+2N+1)/4
Derivation:
For the series-
Nth term can be written as-
Here,
and 1+3+5+….+(2*N-1) are in A.P.
Rewriting the above equation using the formula for A.P. as-
The Nth term of the given series can be generalized as:
Illustration:
Input: N = 2
Output: 2.25
Explanation: (1^3+2^3)/(1+3)
= (1 +8)/4
= 9/4
= 2.25
Below is the implementation of the above problem:
C++
// C++ program to find N-th term // in the series #include <bits/stdc++.h> using namespace std; // Function to find N-th term // in the series double nthTerm( int N) { return ( pow (N, 2) + 2 * N + 1) / 4; } // Driver Code int main() { // Get the value of N int N = 5; cout << nthTerm(N); return 0; } |
Java
// Java code for the above approach import java.io.*; class GFG { // Function to find N-th term // in the series static double nthTerm( int N) { return (Math.pow(N, 2 ) + 2 * N + 1 ) / 4 ; } public static void main(String[] args) { // Get the value of N int N = 5 ; System.out.println(nthTerm(N)); } } // This code is contributed by Potta Lokesh |
Python
# python 3 program for the above approach import sys # Function to find N-th term # in the series def nthTerm(N): return ( pow (N, 2 ) + 2 * N + 1 ) / 4 # Driver Code if __name__ = = "__main__" : N = 5 print (nthTerm(N)) # This code is contributed by hrithikgarg03188 |
C#
// C# program to find N-th term // in the series using System; class GFG { // Function to find N-th term // in the series static double nthTerm( int N) { return (Math.Pow(N, 2) + 2 * N + 1) / 4; } // Driver Code public static void Main() { // Get the value of N int N = 5; Console.Write(nthTerm(N)); } } // This code is contributed by Samim Hosdsain Mondal. |
Javascript
<script> // JavaScript program to find N-th term // in the series // Function to find N-th term // in the series const nthTerm = (N) => { return (Math.pow(N, 2) + 2 * N + 1) / 4; } // Driver Code // Get the value of N let N = 5; document.write(nthTerm(N)); // This code is contributed by rakeshsahni </script> |
Output
9
Time Complexity: O(1)
Auxiliary Space: O(1)