给定一系列其中x,y和n为整数值。任务是找到直到给定级数的第n个项的和。
例子:
Input: x = 2, y = 2, n = 2
Output: 40
Input: x = 2, y = 4, n = 2
Output: 92
方法:给定系列为:
。
因此,我们的问题减少到寻找两个GP系列之和。
下面是上述方法的实现:
C++
// CPP program to find the sum of series
#include
using namespace std;
// Function to return required sum
int sum(int x, int y, int n)
{
// sum of first series
int sum1 = (pow(x, 2) * (pow(x, 2 * n) - 1))
/ (pow(x, 2) - 1);
// sum of second series
int sum2 = (x * y * (pow(x, n) * pow(y, n) - 1))
/ (x * y - 1);
return sum1 + sum2;
}
// Driver Code
int main()
{
int x = 2, y = 2, n = 2;
// function call to print sum
cout << sum(x, y, n);
return 0;
}
Java
// Java program to find the sum of series
public class GFG {
// Function to return required sum
static int sum(int x, int y, int n)
{
// sum of first series
int sum1 = (int) (( Math.pow(x, 2) * (Math.pow(x, 2 * n) - 1))
/ (Math.pow(x, 2) - 1));
// sum of second series
int sum2 = (int) ((x * y * (Math.pow(x, n) * Math.pow(y, n) - 1))
/ (x * y - 1));
return sum1 + sum2;
}
// Driver code
public static void main (String args[]){
int x = 2, y = 2, n = 2;
// function call to print sum
System.out.println(sum(x, y, n));
}
// This code is contributed by ANKITRAI1
}
Python3
# Python3 program to find the sum of series
# Function to return required sum
def sum(x,y,n):
# sum of first series
sum1 = ((x**2)*(x**(2*n)-1))//(x**2 - 1)
# sum of second series
sum2 = (x*y*(x**n*y**n-1))//(x*y-1)
return (sum1+sum2)
# Driver Code
if __name__=='__main__':
x = 2
y = 2
n = 2
# function call to print sum
print(sum(x, y, n))
# this code is contributed by sahilshelangia
C#
// C# program to find the sum of series
using System;
class GFG
{
// Function to return required sum
static int sum(int x, int y, int n)
{
// sum of first series
int sum1 = (int) ((Math.Pow(x, 2) *
(Math.Pow(x, 2 * n) - 1)) /
(Math.Pow(x, 2) - 1));
// sum of second series
int sum2 = (int) ((x * y * (Math.Pow(x, n) *
Math.Pow(y, n) - 1)) / (x * y - 1));
return sum1 + sum2;
}
// Driver code
public static void Main ()
{
int x = 2, y = 2, n = 2;
// function call to print sum
Console.Write(sum(x, y, n));
}
}
// This code is contributed by ChitraNayal
PHP
Javascript
输出:
40
时间复杂度: O(log(n))